Дз по Сетевым моделям
Подготовительные шаги
# Установим рабочую директорию
setwd("~/Documents/GitHub/RProjects_EF/Networks")# Подгрузим необходимые для дальнейшего анализа библиотеки
## install.packages("igraph")
## install.packages("igraphdata")
## install.packages("ggraph")
## install.packages("tidygraph")
## install.packages("DescTools")
library(igraph);
Присоединяю пакет: ‘igraph’
Следующие объекты скрыты от ‘package:stats’:
decompose, spectrum
Следующий объект скрыт от ‘package:base’:
unionlibrary(igraphdata);
library(ggraph);Загрузка требуемого пакета: ggplot2library(tidygraph);
Присоединяю пакет: ‘tidygraph’
Следующий объект скрыт от ‘package:igraph’:
groups
Следующий объект скрыт от ‘package:stats’:
filterlibrary(DescTools);Registered S3 method overwritten by 'data.table':
method from
print.data.table
Присоединяю пакет: ‘DescTools’
Следующий объект скрыт от ‘package:igraph’:
%c%Обработка данных и создание графа
# Загрузим данные для исследования: набор ребер и вершин
edges <- read.csv("edges_1.csv", header=T)
colnames(edges) <- c('from', 'to', 'type1', 'type2', 'weight')
nodes <- unique(edges[c('from', 'type1')])
more_nodes <- unique(edges[c('to', 'type2')])
colnames(nodes) <- c('organisation', 'type')
colnames(more_nodes) <- c('organisation', 'type')
nodes <- rbind(nodes, more_nodes)
nodes <- unique(nodes[c('organisation', 'type')])
rownames(nodes) <- NULL
edges <- edges[c('from', 'to', 'weight')]
# Создадим также набор обратных величин для весов ребер (это пригодится нам в дальнейшем). Исходные веса нам уже не понадобятся
edges$weight <- 1 / edges$weight
net <- graph_from_data_frame(d=edges, vertices=nodes, directed=F)
V(net)$color <- ifelse( V(net)$type=="Business Enterprise", "red",
ifelse( V(net)$type=="Private not for profit", "purple",
ifelse( V(net)$type=="Government", "green",
ifelse( V(net)$type=="Higher Education", "blue", "black")
)
)
)
head(V(net)$color, 10) [1] "red" "red" "red" "red" "red" "red" "purple" "green" "purple" "red" Поясним, почему в дальнейшем будем работать именно с обратными весами: Кратчайший путь и кратчайшее расстояние в данной задаче будут представлять собой не то же самое, что и в задаче с издержками перевозок или длинами расстояний между вершинами в качестве весов ребер. Отрицательные веса мы не используем, потому что алгоритм Дейкстры работает с неотрицательными весами ребер, поэтому далее мы оперируем с обратными весами, т.к., на наш взгляд, этот выбор является наиболее оптимальным для преодоления возникших трудностей.
Исследовательский вопрос
Исследовательский вопрос: Какие есть способы улучшения взаимодействия учреждений высшего образования Новой Зеландии (если это вообще требуется)?
Наше исследование показывает, что возможно повысить эффективность небольших университетов посредством увеличения сотрудничества с крупными, которые в свою очередь имеют тесное сотредничество с бизнесом.
Детали см. в Задании 6.
Анализ датасета
Описание датасета
Датасет представляет из себя множество вершин с качественными характеристиками и множество ребер с числовыми характеристиками (весами).
Вершинами являются организации Новой Зеландии, которые занимаются написанием научных статей в качестве одного из видов деятельности. Качественной характеристикой вершин является вид организации (государственная организации, высшее учебное заведение, коммерческое предприятие и частное некоммерческое предприятие). Всего в датасете 1511 вершин.
Между i-ой и j-ой вершинами (организациями)
существует ребро, если за период 2010-2015 гг. на Scopus была
опубликована хотя бы одна статья, хотя бы один автор которой числится в
организации i, а другой автор – в организации
j. Всего в датасете 4273 ребра.
Вес ребра равен количеству совместных опубликованных научных работ.
Если вес ребра между i-ой и j-ой вершиной
равен 3, то это означает, что за указанный период на Scopus было
опубликовано 3 научные работы, у которых хотя бы один автор числится в
организации i, а другой — в организации j.
Задание 2
При использовании нескольких пакетов для работы с графами не
оказалось возможным интерпретируемо визуализировать граф полностью.
Поэтому для отображения структуры нашей сети найдем 100 самых
центральных по степени вершин и представим связи между ними при помощи
пакета ggraph.
V(net)$degrees <- degree(net)
nodes$degrees <- V(net)$degrees
for_vis_n <- nodes[order(-nodes$degrees),][1:100, 1:2]
for_vis_e <- edges[(edges$from %in% for_vis_n$organisation & edges$to %in% for_vis_n$organisation),]
for_vis_net <- graph_from_data_frame(d=for_vis_e, vertices=for_vis_n, directed=F)
V(for_vis_net)$degrees <- degree(for_vis_net)
for_vis_net %>%
ggraph(layout='graphopt') +
geom_node_point(aes(color = type, size=round(degrees/20))) +
geom_edge_link(alpha = 0.05) +
theme_void() +
ggtitle("Network of New Zealand organisations")
Как можно увидеть, среди 100 самых центральных вершин с количественной точки зрения преобладают организации государственного сектора, однако самыми крупными здесь являются новозеландские университеты. Первые 5 мест по числу совместных научных работ принадлежат именно им, лидером по данному показателю является Университет Окленда, самый крупный и престижный университет Новой Зеландии.
Рассчитаем базовые параметры нашего графа. Так как весами дуг в данном случае является число совместных работ, то есть “сила связи” двух вершин, будем использовать обратные веса для подсчета центральностей через кратчайшие пути. Это довольно разумно, так как от написания дополнительной общей работы прирост в силе связи двух организаций должен монотонно снижаться, как и разница в пути до соседа.
#Считаем базовые параметры графа
# Density
# The proportion of present edges from all possible ties.
p <- edge_density(net)
# связность сети
no <- igraph::components(net)$no # в пакете statnet такое же название
csize <- igraph::components(net)$csize
csize [1] 1463 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[21] 2 2 3 2# Diameter (longest geodesic distance) (если несколько компонент, то диаметр самой большой)
# Note that edge weights are used by default, unless set to NA.
diam <- diameter(net, weights=NA)
diam_w <- diameter(net)
path <- get_diameter(net, weights=NA)
path_w <- get_diameter(net)
path+ 7/1511 vertices, named, from 21a717d:
[1] Dairy Production Systems Ltd. Straven Road Veterinary Centre AgResearch
[4] Auckland Council Auckland District Health Board New Zealand National Eye Bank
[7] Project Litefoot Trust path_w+ 9/1511 vertices, named, from 21a717d:
[1] Dairy Production Systems Ltd. Straven Road Veterinary Centre AgResearch
[4] Massey University University of Auckland Victoria University of Wellington
[7] GNS Science ECoast Limited Dumpark Data Science # рассчитаем кратчайшие пути
# Average path length
# The mean of the shortest distance between each pair of nodes in the network
# (in both directions for directed graphs).
m_dist <- mean_distance(net, weights=NA)
m_dist_w <- mean_distance(net)Плотность нашего графа составляет 0.0037. Такая низкая плотность (вероятность образования связи) довольно естественная для вероятности написания научной работы. Наша сеть имеет 24 компонент связности: одна главная, соединяющая практически все вершины, а все остальные имеют по 2-3 вершины. Диаметр (наибольший из кратчаших путей) имеет длину 4.01, или 6, если брать единичные веса для всех дуг.
Изучим соседство самой центральной вершины — Оклендского Университета (с кем чаще всего взаимодействует наиболее престижный ВУЗ страны):
# We can also easily identify the immediate neighbors of a vertex.
# The 'neighbors' function finds all nodes one step out from the focal actor.
# To find the neighbors for multiple nodes, use 'adjacent_vertices()'.
d <- data.frame(neighbors(net, V(net)["University of Auckland"], mode="total")$type)
groups <- as.data.frame(table(d))[, 2]
pie(groups, labels=paste0(as.data.frame(table(d))[, 1], ', ',round(groups/sum(groups)*100, digits=1), '%'),
col=c(5, 2, 3, 4), main='Neighbors of University of Auckland')
# To find node neighborhoods going more than one step out, use function 'ego()'
# with parameter 'order' set to the number of steps out to go from the focal node(s).
neigh2 <- data.frame(ego(net, order = 2, nodes = V(net)["University of Auckland"])[[1]]$type)
groups2 <- as.data.frame(table(neigh2))[, 2]
pie(groups2, labels=paste0(as.data.frame(table(neigh2))[, 1], ', ',round(groups2/sum(groups2)*100, digits=1), '%'),
col=c(5, 2, 3, 4), main='Two-step neighbors of University of Auckland')
Довольно ожидаемо, что чаще всего в написании научных работ такой успешный университет сотрудничает с индустрией. Это подтвеждает наше предположение о том, успех научной работы зависит от работы с бизнесом. В ближайшем окружении данной организации также принято вести исследования с индустрией.
Сравним нашу сеть с теоритическими моделями случайного графа на основе распределения числа их соседей, диаметра, среднего кратчайшего пути и числа компонент связности. Начнем с модели случайного графа Эрдеша-Реньи.
#Генерируем модели случайного графа erdos.renyi
p <- edge_density(net)
random_model <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))par(mfrow = c(1, 1))
gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
gl[[i]] <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
m[i] <- mean_distance(gl[[i]])
d[i] <- diameter(gl[[i]])
a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 
diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 
number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
Как можно заметить, все рассматриваемые показатели нашей сети значимо отличаются от модельных, значит, структуру нашей сети нельзя описать данным образом.
Обратимся к модели “Малого мира” с регулярной решеткой. Однако в этом случае сперва нужно подобрать гиперпараметр — долю переприсоединенных дуг.
#Генерируем модели случайного графа с регулярной решеткой
n_of_nei <- mean(degree(net))
diam_net <- diameter(net, weights=NA)
#Ищем оптимальное значение p
mean_dist_net <- mean_distance(net)
model <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
res <- rep(NA, 100)
for (i in 1:100){
model[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = i/100)
m[i] <- mean_distance(model[[i]])
d[i] <- diameter(model[[i]])
res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2)
}
# p = 0.99
random_model <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))par(mfrow = c(1, 1))
gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
gl[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
m[i] <- mean_distance(gl[[i]])
d[i] <- diameter(gl[[i]])
a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 
diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 
number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
m[i] <- mean_distance(model[[i]])
d[i] <- diameter(model[[i]])
res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2)
}
plot(x=c(1:40)/10, y=res)
#power=2.15
random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))par(mfrow = c(1, 1))
gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
m[i] <- mean_distance(gl[[i]])
d[i] <- diameter(gl[[i]])
a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 
diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 
number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
Аналогично предыдущему случаю, данная модель плохо описывает структуру нашего графа. Значимо совпадает лишь диаметр, так как по нему в том числе происходил подбор гиперпараметра.
Рассмотрим также схожесть с моделью Барабаши-Альберта, включающей предпочтительное присоединение к наиболее центральным вершинам.
# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
m[i] <- mean_distance(model[[i]])
d[i] <- diameter(model[[i]])
res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2)
}
#power=2.15
random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))par(mfrow = c(1, 1))
gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
m[i] <- mean_distance(gl[[i]])
d[i] <- diameter(gl[[i]])
a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 
diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 
number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
Как мы получили, данная модель тоже не подходит для описания структуры новозеландской сети: все статистически значимо отличается, кроме параметра, по которому проходил подбор гиперпараметра.
Выводы
Выводы по Заданию 2: Ни одна из теоретических моделей, известных нам, не описывает структуры нашего графа достаточно точно.
Задание 3
В этом задании нам предлагается посчитать различные меры центральности вершин и сделать содержательные выводы на основе полученных расчетов.
- Замечание
-
Для анализа используем обратные веса, т.к. их использование делает осмысленным расчет центральности по близости и кратчайшему пути, но не искажает остальных мер центральности вершин.
Центральность по степени
Для начала посчитаем центральность по степени:
deg <- degree(net)
# plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=deg)Теперь построим гистограмму распределения степеней вершин:
# гистограмма степеней вершин
hist(deg, main="Histogram of node degree", breaks=50, prob=TRUE) 
# распределение степеней вершин
mean(deg) # Средняя степень вершины по графу[1] 5.655857# ~ 5.66
Mode(deg) # Модальная степень вершин графа[1] 1
attr(,"freq")
[1] 599# 1 -> 599 раз
median(deg) # Медиана степеней вершин[1] 2# ~ 2
top_10_degree <- tail(sort(deg), 10) # топ-10 по степеням
top_10_degree # в топе - 7 университетов, 3 гос. учреждения Canterbury District Health Board AgResearch University of Waikato
121 126 136
Auckland District Health Board AUT University Victoria University of Wellington
143 145 204
University of Canterbury Massey University University of Otago
241 310 406
University of Auckland
551 Вывод: Центральность вершин по степени не зависит от
весов. Подавляющее большинство вершин имеет степень, меньшую
50. Так, медиана кол-ва соседей равняется 2. В среднем у
вершины такого графа степень равна 5.66. Наиболее часто встречающаяся
степень вершины — 1, которая встречается 599 раз. Если мы посмотрим 10
вершин с наибольшим числом соседей, то окажется, что 7 из них являются
университетами, в числе которых крупнейший — университет Окленда
(степень вершины максимальная — 551). Оставшиеся 3 организации являются
государственными: 2 департамента здравоохранения и 1 исследовательская
компания. Степень у всех вершин, входящих в топ-10, > 100.
Центральность по близости
Далее рассчитаем центральность по близости двумя
способами: В первом варианте все веса ребер графа являются
1, в другом используются обратные веса ребер.
clos1 <- closeness(net, weights=NA) # Первый способ - без учета весов
clos1 45 South Management Ltd.
0.0002281022
Abacus ALS
0.0002440810
AbacusBio Ltd.
0.0002704164
ABB Power Quality
0.0002391772
ABI Rehabilitation New Zealand Ltd.
0.0002207506
AC Research Associates
0.0002610285
Academic Colleges Group New Zealand
0.0002593361
Accident Compensation Corporation
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Action on Smoking and Health New Zealand
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Active Health
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Acurity Health Group ltd.
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Ade Consultants
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Adidas Sports Medicine
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Adis International Ltd.
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Advanced Clinical Skills Centre
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AECOM
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AECS Ltd.
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Aerocool Ltd.
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Aeroqual Ltd.
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Affinity Services
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AFT Pharmaceuticals Ltd
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AFTpharmaceuticals
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Agencies for Nutrition Action
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Agile Utilities New Zealand Ltd
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Agknowledge Ltd.
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AgResearch
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Agri-Optic NZ Ltd.
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Agribusiness Group
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AgriGenesis Biosciences Ltd
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AgriHealth NZ Limited
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Agrimm Technologies Ltd
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AgriNova NZ Ltd
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AgriQuality Limited
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Agvance Marketing Ltd.
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Air New Zealand
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Air Quality Ltd.
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Airborne Honey Ltd.
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Akaroa Medical Centre
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Ako Aotearoa National Centre for Tertiary Teaching Excellence
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Akoranga Integrated Health Clinic
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Alan Bell and Associates
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Albany Basin Accident and Medical Centre
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Alcohol Advisory Council of New Zealand
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Alcohol Harm Minimisation Advisory Group
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Alcohol Healthwatch Trust
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Alexandra Lions Club
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Alexandra Medical Centre
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Alfriston College
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All Seasons Pharmacy
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Allan Planning and Research Ltd.
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Allen & Clarke Policy and Regulatory Specialists Limited
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Alphalabs
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Alpine and Polar Processes Consultancy
0.0002491281
Alzheimers Northland
1.0000000000
Amalgamates Solutions and Research Ltd.
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Amity Health Centre
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Ancare New Zealand Ltd.
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Ancare Scientific Ltd
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Anexa FVC
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Anglesea Medical Properties Ltd
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Animal Dermatology NZ
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Animal Health Board New Zealand
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Animals and Marine Surveillance and Investigation Team
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Animation Research Limited
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Antarctic Heritage Trust
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Antarctica New Zelaand
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Antarctica Scientific Limited
0.0002307337
Antipodean Pharmaceuticals
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Aorangi Veterinary Services
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Aotea Pathology Ltd.
0.0002942042
Aotearoa Alcohol and Other Drug Consumer Network
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AP EnerTec Ltd.
1.0000000000
Applied Engineering Research Ltd.
0.0002252760
Applied Research and Technologies Ltd.
0.0002282584
Applied Research Associates New Zealand
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AquaBio Consultants Ltd.
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Aquaculture New Zealand
0.0002572016
Aqualinc Research Ltd.
0.0002802691
Aquanet Consulting Ltd.
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Aquatic Research Solutions Ltd.
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Aranui High School
0.0002283626
ARANZ Geo Ltd
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ARANZ Medical Scanning
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Areograph Ltd.
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ARH Construction
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Aroa Biosurgery
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Arohanui Hospice
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Arotec Diagnostics Ltd.
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Ascot Angiography
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Ascot Women's Cancer Centre of New Zealand
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Asia New Zealand Foundation
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Asphalt Products Limited
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Aspiring Veterinary Service Ltd
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ASR Limited Martine Consulting and Research
0.0002367985
Assa Abloy New Zealand Ltd
0.0002491901
Assistive Technology Ltd.
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Assurity Consulting Ltd
0.0002324500
AsureQuality
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AsureQuality Ltd.
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At the Vets
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Atkinson and Rapley Consulting
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Atlantis HealthCare
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Auckland-Waikato Fish and Game Council
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Auckland Astronomical Society
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Auckland Botanic Gardens
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Auckland Breast Centre
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Auckland City Mission
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Auckland Clinical Studies Ltd.
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Auckland Council
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Auckland Cricket Assn Inc
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Auckland Dermatology
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Auckland District Health Board
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Auckland Eye
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Auckland Heart Group
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Auckland Institute of Studies
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Auckland International Airport Limited
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Auckland Museum
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Auckland Refugee Community Coalition
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Auckland Regional Council
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Auckland Southern Cross Hospital Group
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Auckland Transport
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Auckland Zoo
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Aurecon
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Australian and New Zealand College of Anaesthetists
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AUT University
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Automation Design Ltd
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Aviation Industry Association of New Zealand Inc
1.0000000000
Avivet Ltd
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Avocado Industry Council
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Babbage Consulting Ltd.
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Ballance Agri-Nutrients Limited
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Bank of Scotland
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Bartonk Solutions
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Batten Animal Research Network
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Baxter Healthcare Limited
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Bay Audiology
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Bay of Plenty District Health Board
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Bay of Plenty Polytechnic
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Bay of Plenty Regional Council
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Bay Urology
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Bayer CropScience New Zealand
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Bayleys Property Services
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BC Consulting Ltd.
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BCRL Energy Limited
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Beca
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Beef and Lamb New Zealand
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Bennett Scientific
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Benthic Science Ltd.
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Berryworld Ltd
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Best Practice Advocacy Centre
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Beta Solutions
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Bethesda Care
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Betta Bees Research Ltd
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Better Border Biosecurity
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BHU Future Farming Centre
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Bickler Consultants Ltd.
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BikeNZ
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Bio Soil and Crop Ltd
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Bioactives Research New Zealand
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Biodiscovery New Zealand Ltd.
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Biomarine Ltd.
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Biomatters Ltd.
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Biometrics Matters Ltd
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Biopolymer Network Ltd
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Biosecurity New Zealand
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BioSylve Forest Science NZ Ltd.
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BirdLife Global Seabird Programme
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Blind Foundation
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BLIS Technologies Ltd.
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Blue Water Marine Research
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Blues Rugby Club
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Bodeker Scientific
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Body Aid Clinic Ltd
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Boffa Miskell Ltd
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Bomac Laboratories Ltd
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Boulcott Hospital
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Braemar Hospital
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BRANZ Ltd.
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Bream Bay Medical Centre
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Breast Care and Screening Services
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Breast Surgeons' Society of New Zealand
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Breen Consulting
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Brian Ricketts Geological Consulting Limited
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Broadway Medical Centre
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Broadway Surgical Clinic
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Broken Hills Gold Co
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Brownrigg Agriculture
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Bruce Shallard and Associates
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Bunnythorpe School
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Cadwallader Tree Consultancy
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Cahill Animal Hospital
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CAL Engineering Management
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Callaghan Innovation
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Cambridge Clinic
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Cambridge Veterinary Services
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Cameron Medical Clinic
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Campbell and Associates Ltd.
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Cancer Control Council of New Zealand
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Cancer Society of New Zealand
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Canterbury Charity Hospital Trust
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Canterbury Civil Defence and Emergency Management Group
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Canterbury District Health Board
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Canterbury Earthquake Recovery Authority
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Canterbury Health Ltd
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Canterbury Medical Imaging
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Canterbury Museum
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Canterbury Rugby Football Union and Crusaders
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CanZealand Geoscience Ltd
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Cape Kidnappers and Ocean Beach Wildlife Preserve
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Cape Sanctuary
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Capital and Coast District Health Board
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Capital Eye Specialists
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Capital Research
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Carbon Partnership
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Cardiac Inherited Disease Group
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Care of Orca Research Trust
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Carey Baptist College
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Carroll Consulting ltd
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Carson Associates Ltd.
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Carter Holt Harvey Ltd.
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Carter National Observatory
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Cashmere Health
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Catch Ltd.
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Catmed
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Cawthron Institute
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CBG Health Research Limited
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Centennial Health
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Center for Backyard Astrophysics
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Central and Southern New Zealand Craniofacial Program
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Central City Vets
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Central Otago Tourism
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Central Stories Museum
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CentralMed
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Centre for Backyard Astrophysics
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Centre for Clinical Research and Effective Practice
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Centre for Dairy Excellence
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Centre for Minerals Environmental Research (CMER)
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Centre for Research Evaluation and Social Assessment
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Centre for Youth Health in South Auckland
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CH and Associates
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ChangeMakers Refugee Forum
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Chatham Rock Phosphate Ltd.
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Chemipreneur Ltd.
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Chemistry Communications
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Chiefs Super Rugby Franchise
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Child and Youth Health
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Child Poverty Action Group
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Chilton Saint James School
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Chiptech Ltd
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Christchurch City Council
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Christchurch Emergency Care Foundation
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Christchurch Polytechnic Institute of Technology
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Christchurch Psychologists' Office
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Christchurch Vascular Group
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City Care Ltd
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City Fitness
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Civil Aviation Authority
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Claro
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ClearSight Consultants Ltd
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Clement and Associates Ltd
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Clendon Burns and Park Consulting Engineers
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CLIMsystems Ltd.
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Clinical Horizons
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Clinical Systems
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Clutha Veterinary Association
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Coast and Catchment Ltd
0.0002648305
Coast to Coast Health Centre
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Coastal and Aquatic Systems Ltd
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Coastal Systems (NZ) Ltd.
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Coastline Consultants
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Cognition Education Limited
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Cognosco
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Colgate-Palmolive Ltd
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Colin Christian Ltd.
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Collins Carriers Ltd.
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Colmar Brunton
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Columba College
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Common Ground Ltd
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Commtest Instruments Ltd
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Community Clinic for Sexual Health and Contraception
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Compac Sorting Equipment Ltd.
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Compac Technologies
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Compass Health
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Compusoft Engineering Limited
0.0002593361
Compusoft Engineering Ltd.
0.0002594034
Comtel System Ltd.
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Comvita New Zealand Ltd.
0.0002774695
Connectos Consulting
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Connovation Ltd.
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Conservation and Environmental Management
0.0002364066
Construction Techniques Ltd.
0.0002685285
Consulting Dietitians Ltd.
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Contact Energy Ltd.
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Contract Landscapes Ltd
0.0002066543
CORE Education Ltd.
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Cosgrove
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Counties Manukau District Health Board
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Covec Ltd
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CPG New Zealand Ltd.
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Crawford Medical Centre
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CRL Energy Ltd.
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Cromwell College
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Cropmark Seeds Limited
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Crown Fibre Holdings Limited
1.0000000000
CURT St George's Medical Centre
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Cuttriss Consultants Ltd
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Cymbiotix Group Limited
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Cyperus Ltd
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Dairy Consultants Ltd.
0.0002070822
Dairy Goat Co-operative (NZ) Ltd.
0.0002693240
Dairy Production Systems Ltd.
0.0001720282
DairyNZ
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David Butler Associates Ltd
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Davidson Environmental Ltd.
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DaVinci Clinic
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DCM Process Control Ltd.
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DEA Research Software Surgery Ltd.
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Deepwater Group Ltd
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DeerNZ
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Deloitte
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Department of Conservation
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Department of Corrections
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Development Action
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Development By Design
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Devon Medical Centre
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DHI Water and Environment
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Diabetes Otago Inc
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Diagnostic Laboratory
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Diagnostic Medlab
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Digestive Health Services
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Digital Sensing Limited
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Disability Connect
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Disability Resource Centre
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Diversity NZ
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DM Consultants
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DNA Investments Ltd.
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Dnature diagnostics and research Ltd.
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Doctors for Sexual Abuse Care
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Donaghys Industries
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Donald Beasley Institute
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Dorothy-Jean and Associates
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Dovedale Ltd.
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Downer EDI Works Limited
0.0002273244
Dr. Malcolm McKellar Ltd.
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Dragonfly Ltd.
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Drummond Food Science Advisory Ltd.
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Dumpark Data Science
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Duncan Cotterill
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Dunedin City Council
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Dunedin Heat Pumps Limited
0.0002491901
Dunedin South Veterinary Clinic
0.0002430134
Dunning Thornton Consultants Ltd.
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Dynamic Controls Ltd.
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Dynatest
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Dyspraxia Support Group of New Zealand
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Earthquake Commission
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Earthtech Consulting Limited
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Eastern Institute of Technology
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Eastern Region Fish and Game
0.0002347969
Eastern Suburbs Association Football Club (ESAFC)
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Eastland Veterinary Services Ltd.
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Eaton Power Quality Ltd.
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ECG Consultants
0.0002430134
Eco-Vista Photography and Research Ltd.
0.0002871088
Eco Nomos Ltd.
0.0002340824
Eco Research Associates Ltd
0.0002837684
ECoast Limited
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EcoGecko Consultants Ltd.
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Ecosynergy Group Ltd (EGL)
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Ectus Ltd
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Edmund Lawler and Associates Limited
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Education House
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Education Review Office
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Educational Leadership Project
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Electricity Authority
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Eli Lilly and Company (New Zealand) Limited
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Elmwood Orthopaedics
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Eltham District Veterinary Services
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Endoscopy Auckland
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Energy Efficiency and Conservation Authority
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Energy Solution Providers Ltd.
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EnForm Tech
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Enigma Publishing Ltd.
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Ensys Ltd
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Entecol Ltd.
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Enviro-Mark Solutions Ltd.
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Enviro Research
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Environment Canterbury
0.0003033060
Environment Protection Authority(EPA)
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Environmental Management Services
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Environmental Restoration Ltd
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ENZO Nutraceuticals Limited
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Epi-interactive
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Epsom Girls Grammar School
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Equine Health Association
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ERA Ecology
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Erin Park
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ESR
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Etec Crop Solutions
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Eudyptes EcoConsulting Ltd
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Explore NZ
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Eye Institute
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Far North District Council
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Farm Cove Observatory
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Feilding Medical Centre
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FEM Ltd.
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Fern Research Foundation
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Ferndale School
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Fertility Associates
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Financial Markets Authority
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Fish and Game NZ
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Fisher and Paykel Appliances
0.0002593361
Fisher and Paykel Healthcare Ltd.
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Fishing Vessel Management Services Ltd.
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FitzRoy of Merivale
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Fletcher Construction Co
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FMR GROUP LTD
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Fonterra
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Food and Bio-based Products Group
0.0002506894
Food and Health Group
0.0002506894
Foot Science International Ltd.
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Forensic and Industrial Science Ltd
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Forest and Bird
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Forever Beech Ltd.
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Foundation for Arable Research
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Foundation for Research Science and Technology
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Fox and Associates-Consulting Surveyors
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Fred Hollows Foundation
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Fresenius Medical Care Australia Pty Ltd (New Zealand Branch)
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Freshport NZ Ltd
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Frontier Global Ltd.
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Fruitfed Supplies
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Fruition Horticulture
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FullSpectrum Ltd.
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Fulton Hogan Ltd.
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Future Forests Research
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Future Steps
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FuturebyDesign Ltd.
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FutureMATH Ltd.
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Gallagher Animal Management Systems
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Gambling Helpline
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Genesis Research & Development Corporation Ltd
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Genetic Technologies Ltd.
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Gentrack Limited
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Geoenvironmetal Services
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GEOKEM
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Geomarine Research
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Geoscience Consulting Ltd
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Geotech Consulting Ltd
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Geothermal Engineering Ltd
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Geoventures Limited
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GF McLaren Research Limited
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GHD Centre Level Napier St.
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GHD Limited
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Gillies McIndoe Research Institute
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Gisborne District Council
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Glass Earth Gold Ltd
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Glenview Medical Centre
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Global Action for Health Equity Network (HealthGAEN)
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Global Public Health Company Ltd
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GNS Science
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Golden Bay Cement
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Golder Associates (NZ) Ltd
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Good Life Research Centre Trust
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Google
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Greater Wellington Regional Council
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Green Lane Hospital
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Greenweaver Architecture Ltd
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Greerton Early Childhood Centre
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Gribbles Veterinary
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GroPlus Ltd.
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Ground Investigation Ltd
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Growth Solutionz
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Guardian Health Care (Bupa)
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Hagley Community College
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Hally Labels
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Hamilton Eye Clinic
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Hamilton Sacred Heart College for Girls
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Hamilton Veterinary Services
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Hamilton Zoo
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Hanham Consultants
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Hanmer Clinic Tauranga
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Hapai Te Hauora Tapui Ltd
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Harker Underground Construction Limited
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Harris Consulting
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Hauora Heretaunga
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Hauora Waikato Group
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Hauraki Maori Trust Board
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Hawke's Bay Alcohol and Drug Service
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Hawke's Bay District Health Board
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Hawke's Bay Regional Council
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Hawkins Watts
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Health Alliance
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Health Care Aotearoa
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Health New Zealand Ltd.
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Health Outcomes Associates Ltd.
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Health Partners Consulting Group
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Health Promotion Agency
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Health Quality and Safety Commission
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Healthscope Laboratories
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HealthWEST
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Heart Foundation of New Zealand
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Heavy Engineering Research Association
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HEB Construction
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Heinz Wattie's
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Heke Consulting
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Helios Integrative Medical Centre
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Hemptech
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Henderson Medical Centre
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Henderson Valley Primary School
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Hepatitis Foundation of New Zealand
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Herbert Morton Accountants
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Heretaunga Health
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Heritage New Zealand Pouhere Taonga
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High Performance Sport New Zealand
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Highnam Associates Ltd.
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Hill Laboratories Ltd.
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Hiway Geotechnical
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HodderBalog Social and Scientific Research
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Holcim (NZ)
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Holmes Consulting Group
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Holmes Fire and Safety
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Horizons Regional Council
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Horowhenua Community Practice
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Horowhenua Library Trust
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Horteye Ltd
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HortPlus
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Hospice New Zealand
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Hospice Palliative Care Education
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Hospice Waikato
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Hot Solutions Ltd.
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Humes Pipeline Systems
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Huntly Community Link
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Hurricanes Rugby
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Hush Interiors Ltd
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Hutt Valley District Health Board
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Hyland Consultants
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Hyland Fatigue Earthquake Engineering
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Hyperbaric Health
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IAG
0.0002391772
Ian Kusabs and Associates Limited
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Ian McLean Consultancy Services Ltd.
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Ichthyo-niche
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IGENZ Ltd
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ILR
0.0002607562
Immunisation Advisory Centre
0.0002619859
Inclusive Education Action Group
0.0002594034
Independent Petroleum Laboratory
0.0002638522
Indufor Asia-Pacific Ltd
0.0002258866
Infoics Limited
0.0002297266
Inform Planning Ltd
0.0002635741
Infrastructure Decisions Limited
0.0002571355
Inglewood Veterinary Services
0.0002433682
Injury Prevention Aotearoa
0.0002656748
Inland Revenue
0.0002419550
Innate Immunotherapeutics Limited
0.0002816901
Innate therapeutics
0.0002353495
Inner City Women's Group
0.0002593361
Inner Zest Ltd.
0.0002593361
INR Online Ltd
0.0002157032
Insect Science Solutions
0.0002331002
Insights MSD
0.0002044154
Inspiring Ltd.
0.0002755580
Institution of Professional Engineers New Zealand
0.0002595380
Intellectual Property Office of New Zealand
0.0002348520
Intensive Care Flight Paramedic
0.0002272211
Interactionz
0.0002308403
InterAg
0.0002832861
International Animal Welfare Consultants Limited
0.0002430134
International Earth Sciences IESE Ltd.
0.0002690342
International Pacific College
0.0002430134
International Student Ministries of New Zealand
0.0002492522
International Telematics Ltd.
0.0002432498
Interpine
0.0002256827
Interpine Forestry Ltd
0.0002260398
Intus Digestive and Colorectal Care
0.0002491901
Invenco Group Ltd.
0.0002593361
Investigation Geology Ltd
0.0002392344
IPENZ
0.0002641310
Irrigation New Zealand Inc.
0.0002285192
Isolytix
0.0002491901
IZON Science Ltd.
0.0002885170
Jackett Consulting
0.0002053810
Jacobs Engineering
0.0002596054
Jade Software Corporation
0.0002590003
James and Monroe
0.0002480774
JMR Distributors Ltd
0.0002430134
John Jones Steel
0.0002686728
John Wood Consulting
0.0002688172
Johne's Management Limited
0.0002500000
Jowett Consulting Ltd.
0.0002316423
JRA (NZ) Ltd.
0.0002593361
Julian King and Associates Limited
0.0002284148
Ka Mau Te Wero
0.0002283105
Kaikorai Valley College
0.0002491901
Kaikoura Ocean Research Institute Inc.
0.0002616431
Kaipaki Veterinary Services
0.0002430134
Kaipara District Council
0.0002434275
Kapiti Coast District Council
0.0002371354
Karori Sanctuary Trust
0.0002486944
Katoa Ltd
0.0002808200
Kea Conservation Trust
0.0002333178
KEA Consultant
1.0000000000
Keratec Ltd.
0.0002547771
Kidney Health New Zealand
0.0002794077
Kina Families and Addictions Trust
0.0002634352
Kinetic Engineering Design
0.0002593361
Kingdom Clinic
0.0002495010
Kiwi Well Evaluation Ltd
0.0002560164
Kiwi Wildlife
0.0002200220
Kiwicap Research Ltd
1.0000000000
Kiwikiwi Research and Evaluation Services
0.0002070393
Kono Horticulture Limited
0.0002535497
Koru Environmental Consultants Ltd
0.0002288330
Koti Technologies
0.0002391772
Kumeu Observatory
0.0002905288
Kurahaupo Consulting
0.0002283105
KVB Kunlun New Zealand Limited
0.0002430134
Labtests
0.0002794077
Lake Hawea Institute of Cryodynamics
0.0002466091
Lakes District Health Board
0.0002837684
Land Information New Zealand
0.0002661698
Landcare Research
0.0003425831
Landcorp Farming Limited
0.0002773925
Langimalie Clinic
0.0002273244
LanzaTech NZ Ltd.
0.0002508781
Lassey Research and Education Ltd
0.0002278423
Lateral Technology
0.0002593361
Laura Fergusson Trust
0.0002507523
Law Commission
0.0002359604
LeaderBrand Produce Ltd.
0.0002281022
Learning for Sustainability
0.0002896871
Leather & Shoe Research Association of New Zealand
0.0002477701
Leinster Orthopaedic Centre
0.0002039568
Levare Limited
0.0002619859
Levin and Horowhenua Veterinary Centre
0.0002430724
Lewis and Barrow Ltd.
0.0002282584
LIC
0.0002873563
Life Technologies Ltd.
0.0002391772
LightBox Psychology Services
0.0002590003
Lincoln Agritech Ltd.
0.0002776235
Lincoln University
0.0003394433
Lincolne Scott Ltd.
0.0002391772
Lindis Consulting
0.0002302026
Linnaeus Laboratory
0.0002268088
Litmus
0.0002761668
Livestock Solutions and Services
0.0002430134
Living Cell Technologies NZ Ltd.
0.0002600104
Local Government New Zealand
0.0002396358
Logjiztix Ltd
0.0002021019
Lowe NZ
0.0002278423
Lucas Industries (NZ) Ltd.
0.0002593361
LWT Animal Nutrition Ltd.
0.0002430724
MacMurray Hypertension Clinic Ltd
0.0002602134
MAGAK
0.0002227668
Magic Sparks Early Learning and Development Centre
0.0002562132
Magritek Limited
0.0002658161
Makoura College
0.0002359604
Malaghan Institute of Medical Research
0.0003013864
Male Survivors of Sexual Abuse Trust
0.0002391772
Manaaki Te Awanui
0.0002764722
Manaia Health Primary Health Organisation
0.0002352941
Manawatu Diagnostics
0.0002430134
Mangere Community Health Trust (Primary Health Organisation)
0.0002631579
Manukau Institute of Technology
0.0003097893
Manukau SuperClinic
0.0002593361
Manurewa South School
0.0002593361
Maori Hill Clinic
0.0002491901
Maori Pharmacists Association
0.0002767017
Maramatanga Consultants Ltd
0.0002430134
Marine Fisheries Research Services Limited
0.0002246181
Marine Wildlife Research Ltd
0.0002623983
Marinoto Clinic
0.0002507523
Mark L Batchelar Consulting Engineers
0.0002391772
Market Economics Ltd.
0.0002430134
Marlborough Wine Research Center
0.0002823264
MARS Bioimaging Ltd
0.0002614379
Marshall Day Acoustics Ltd.
0.0002686006
Mary Potter Hospice
0.0002633658
Massey University
0.0003767898
Masters Consulting Ltd.
0.0002246181
Matakina Technology Ltd
0.0002533570
Matamata Medical Centre
0.0002600104
Matamata Veterinary Services Ltd
0.0002477087
MBCentury Ltd
0.0002593361
McConnell Dowell Constructors Ltd.
0.0001974334
McLaren Research Ltd.
0.0002280502
McManus Geotech Ltd.
0.0002187705
Medical Council of New Zealand (MCNZ)
0.0002069965
Medical Research Institute of New Zealand
0.0003109453
Medlab Central
0.0002808989
Melanoma Unit
0.0002604845
Member International Neuropsychological Society
0.0002491901
Mental Health Education Resource Centre
0.0002391772
Mental Health Foundation of New Zealand
0.0002751789
MercyAscot Hospitals
0.0002870264
Meridian Energy Ltd.
0.0002419550
Mesynthes Ltd.
0.0002630887
Meteorological Service of New Zealand Ltd.
0.0003009329
Methanex
0.0002434275
MetOcean Solutions Ltd.
0.0002566735
Microfossil Research Ltd
0.0002996704
MidCentral District Health Board
0.0003147624
Midland MRI
0.0002308403
Midland Regional Forensic Services
0.0002593361
Midlands Health Network
0.0002600780
Midwifery Council of New Zealand
0.0002498751
Mighty River Power Ltd.
0.0002800336
Millar Instruments
0.0002630195
Milton Health Centre
0.0002493144
Ministry for Primary Industries
0.0003301420
Ministry for Primary Industry
0.0002587992
Ministry for the Environment
0.0003100775
Ministry of Business Innovation and Employment
0.0002691066
Ministry of Civil Defence and Emergency Management
0.0002274795
Ministry of Education
0.0003069368
Ministry of Foreign Affairs and Trade
0.0002572678
Ministry of Health
0.0003163556
Ministry of Justice
0.0002865330
Ministry of Pacific Island Affairs
0.0003051572
Ministry of Social Development
0.0002794857
Ministry of Transport
0.0002365184
Mission Heights Primary School
0.0002246181
MLB Consulting Engineers
0.0002391772
Molehill Astronomical Observatory
0.0002905288
Moorhouse Medical Clinic
0.0002327747
Morrison Consultants Ltd
0.0002165440
Motu Economic and Public Policy Research
0.0003075977
Mountains to Sea Conservation Trust
0.0002648305
MSD Animal Health Ltd
0.0002446184
Mt. Albert Psychological Services Ltd
0.0002133106
Mulgor Consulting Ltd.
0.0002314279
Muscular Dystrophy Association of New Zealand
0.0002820874
MWH New Zealand Ltd
0.0002685285
N-Squared Software
0.0002658161
NaeNae Medical Centre
0.0002201189
National Addiction Centre
0.0002491901
National Association of Steel-Framed Housing Inc
0.0002594034
National Council of Women of New Zealand
0.0002436054
National Heart Foundation of New Zealand
0.0002947244
National Library of New Zealand Te Puna Matauranga O Aotearoa
0.0002366304
National Maori Health Workforce Organisation
0.0002491901
Natural Resource Assessors
0.0002563445
Needle Exchange Programme NZ
0.0002755580
Nelson Forests Limited
0.0002411963
Nelson Marlborough District Health Board
0.0003040438
Nelson Marlborough Fish and Game
0.0002506266
Nelson Marlborough Institute of Technology
0.0003100775
Nelson Marlborough Regional Council
0.0002328831
Neonatal Intensive Care Unit
0.0002491901
NetSafe
0.0002593361
NetValue
1.0000000000
Neuren Pharmaceuticals
0.0002593361
Neurological Foundation of New Zealand
0.0002593361
New Brighton Health Care
0.0002508781
New Image Group Ltd
0.0002593361
New River Ltd
0.0002492522
New Zealand Academy of Sport
0.0003009329
New Zealand Aerial Mapping
0.0002609603
New Zealand Agricultural Greenhouse Gas Research Centre
0.0002478315
New Zealand Agriseeds Limited
0.0002468526
New Zealand AIDS Foundation
0.0002756340
New Zealand Aluminium Smelters Limited
0.0002593361
New Zealand Antarctic Institute
0.0002391772
New Zealand Arable
0.0002300437
New Zealand Association of Optometrists
0.0002508151
New Zealand Avocado Growers Association
0.0002280502
New Zealand BioSecure Entomology Laboratory Research
0.0002446184
New Zealand Blood Service
0.0002772387
New Zealand Brain Research Institute
0.0002988643
New Zealand Breast Cancer Foundation
0.0002507523
New Zealand Centre for Conservation Medicine (NZCCM)
0.0003025719
New Zealand Climate & Health Council
0.0002754821
New Zealand College of Chiropractic
0.0002632272
New Zealand College of Midwives
0.0003027551
New Zealand Cot Death Association
0.0002594034
New Zealand Council for Educational Research (NZCER)
0.0002646903
New Zealand Defence Force
0.0003061849
New Zealand Dental Association
0.0002493144
New Zealand Employment Service and Work and Income New Zealand
0.0001773050
New Zealand Familial Gastrointestinal Cancer Service
0.0002767017
New Zealand Forestry Ltd
0.0002253775
New Zealand Geotechnical Society Ine (NZGS)
0.5000000000
New Zealand Guidelines Group
0.0002579979
New Zealand Gynaecological Cancer Foundation
0.0002534212
New Zealand Heart and Lung Transplant Service
0.0002626050
New Zealand Heavy Engineering Research Association
0.0002693966
New Zealand Homebased Early Childhood Education Association
0.0002493144
New Zealand Institute for Plastic and Cosmetic Surgery
0.0002491901
New Zealand Institute of Community Health Care
0.0002608923
New Zealand Institute of Economic Research
0.0002969121
New Zealand Institute of Medical Laboratory Science
0.0002533570
New Zealand Institute of Rural Health
0.0002754821
New Zealand Kiwi Foundation
0.0002593361
New Zealand Medical Association
0.0002533570
New Zealand Medical Students' Association
0.0002754821
New Zealand National Eye Bank
0.0002268603
New Zealand National LCP Office
0.0002615063
New Zealand Needle Exchange Programme
0.0002793296
New Zealand Nurses Organisation
0.0002799552
New Zealand Olympic Committee
0.0002491901
New Zealand Organisation for Rare Disorders (NZORD)
0.0002491901
New Zealand Parliament
0.0002359604
New Zealand Police
0.0002896032
New Zealand Qualifications Authority
0.0002359604
New Zealand Refining Co. Ltd.
0.0002391772
New Zealand Rheumatology Association
0.0002779322
New Zealand Rugby Union
0.0002651113
New Zealand School Acupuncture and Traditional Chinese Medicine
0.0002391772
New Zealand School of Music
0.0002359604
New Zealand Seafood Industry Council Ltd
0.0002296739
New Zealand Society for Earthquake Engineering (NZSEE)
0.5000000000
New Zealand Spinal Trust
0.0002507523
New Zealand Tertiary College
0.0002632272
New Zealand Timberlands Ltd
0.0001937609
New Zealand Transport Agency
0.0002702703
New Zealand Treasury
0.0002914602
New Zealand Underwater Heritage Group
0.0002308936
New Zealand Veterinary Pathology Ltd.
0.0002461841
New Zealand Winegrowers
0.0002626050
Newman Energy Research
0.0002391772
Newtown Medical Centre
0.0002754821
NextWindow Ltd
0.0002754821
Ngati Porou Hauora
0.0002594034
Ngati Whakaue Tribal Lands Inc
0.0002252760
Nielsen Company
0.0002595380
NIU Development Incorporated
0.0002762431
NIWA
0.0003415301
Norske Skog Tasman
0.0002593361
North Canterbury Veterinary Clinics
0.0002437241
North Shore Hospice
0.0002656748
North Shore International Academy
0.0002477701
Northcott Research Consultants Ltd.
0.0002787068
Northern Cancer Network
0.0002619859
Northern Region IDEA Services
0.0002593361
Northern Regional Alliance
0.0002286760
Northern Southland Veterinary Services
0.0002073828
Northland District Health Board
0.0002968240
Northland Regional Council
0.0002797985
NorthTec
0.0002665245
Novare Design Ltd.
0.0002391772
Numcore Ltd.
0.0002593361
Numinos Ltd.
0.0002593361
Nurse Maude Association
0.0002613013
Nutrigenomics New Zealand
0.0002964720
Nutrition Society of New Zealand
0.0002491901
NZ Oil and Gas
0.0002394636
NZ Parsa Tiling Limited
0.0002391772
NZFOCUS (NZ) Ltd.
0.0002593361
NZX Limited
0.0002593361
O'Kane Consultants (NZ) Ltd
0.0002664535
Oamaru Hospital
0.0002491901
Odyssey House
0.0002593361
Office of the Health and Disability Commissioner
0.0002593361
Office of the Parliamentary Commissioner for the Environment
0.0002556891
Omahu Urology Clinic
0.0002500000
OMV New Zealand Ltd.
0.0002619859
Oncology Surgery Ltd.
0.0002628812
Open Polytechnic of New Zealand
0.0003099814
OPRA Consulting Group
0.0002392917
Optimal Clinical Trials
0.0002562788
Opus International Consultants Ltd
0.0002934272
Oracle New Zealand
0.0002359604
Oral Health Centre
0.0002532928
Orange Consulting
0.0002491901
Orb Solutions
0.0002602134
Organ Donation New Zealand
0.0002656748
Oritain Global Ltd.
0.0002491901
Ornithological Society of New Zealand
0.0002663825
Orokonui Ecosanctuary
0.0002560164
OSPRI
0.0002751032
Otago Community Hospice
0.0002592017
Otago Computational Modelling Group Ltd.
0.0002789400
Otago Daily Times Collective
0.0002491901
Otago Girls High School
0.0002930832
Otago Museum
0.0002759382
Otago Polytechnic
0.0003050641
Otago Regional Council
0.0002437241
Otahuhu College
0.0002763958
Otakaro Pathways Ltd
0.0002356268
Otorohanga Dental Surgery
0.0002491901
OTRS Group Ltd
0.0002607562
Outome Management Services
0.0002593361
P.N. Plimmer and Associ.
0.0002594034
PA Handford and Assoc. Ltd.
0.0002255300
Pacific Brands
0.0002593361
Pacific Edge Biotechnology Ltd.
0.0002823264
Pacific Health Research and Development Foundation
0.0002724796
Pacific Radiology Group
0.0002905288
Pacific Women's Health Research and Development Unit
0.0002627430
Pakuranga Medical Centre
0.0002207993
Palaecol Research Ltd
0.0002888504
Palmerston North City Council
0.0002430724
Palmerston North City Library
0.0002359604
Pansophy Ltd
0.0002328831
Papamoa Pines Medical Centre
0.0002822467
Paraparaumu College
0.0002692515
Paric Limited
0.0002593361
Parkinson's New Zealand
0.0002593361
Parresia Research Limited
0.0002593361
Parsons Brinckerhoff
0.0002593361
Pasifika Horizon Healthcare
0.0002593361
Pasifika Medical Association
0.0002594707
Pasifika Research Ltd
0.0002360718
Pathlab
0.0002513826
Patients First
0.0002494388
Paton-Simpson Associates Limited
0.0002540005
Pattle Delamore Partners Ltd
0.0002392917
Pegasus Health Ltd
0.0002843332
Penny and Associates Ltd
0.0002613013
Perinatal and Maternal Mortality Review Committee
0.0002777778
Petersgate Counselling Centre
0.0002391772
PF Olsen and Company Ltd
0.0002257846
PGG Wrightson Seeds Ltd.
0.0002501251
PHARMAC
0.0002787845
Pharmaceuticol Ltd
0.0002496879
Pharmacy Guild of New Zealand
0.0002593361
PharmTech Service Limited
0.0002765487
Philosophy of Education Society of Australasia
0.0002593361
Photonz Corporation Ltd
0.0002593361
Pictor Ltd.
0.0002593361
Pingar Research
0.0002308936
Pinnacle Group Ltd
0.0002596728
PipeTechnologies
0.0002596054
Pipfruit New Zealand
0.0002507523
Planning Consultants Ltd
0.0002635741
Plant and Food Research
0.0003419973
Plant Protection Chemistry NZ Ltd
0.0002307870
PlusGroup Limited
0.0002363507
Pohatu Penguins
0.0002400384
Polybatics Ltd.
0.0002508151
Porirua City Council
0.0002491901
Ports of Auckland Limited
0.0002594034
Positive Thinking Ltd
0.0002593361
Possum Observatory
0.0002906132
Potter Building Services Ltd.
0.0002764722
Power Co Ltd.
0.0002593361
Power Systems Consultants New Zealand Ltd
0.0001976285
PowerbyProxi Ltd.
0.0002593361
Powerhouse Ventures Ltd
0.0002434867
Practitioners First Limited
0.0002594707
Presbyterian Church of New Zealand
0.0002619859
PriceWaterhouse Coopers (PwC)
0.0002849003
Priestley Structural Engineering
0.0002691790
Private Endodontic Practice
0.0002491901
ProCare Health Limited
0.0002638522
Prohealth Physiotherapy Ltd
0.0002493144
Promisia Ltd
0.0002492522
Proteus Wildlife Research Consultants
0.0002568053
Psychological Service
0.0002593361
Psychology Centre
0.0002599428
Pultron Composites Ltd.
0.0002336449
Pyrotek
0.0002403268
Q-Bit Ltd.
0.0002425418
QE Health
0.0002619859
Qnique Ltd
0.0002806624
QStar Solutions Ltd.
0.0002396932
Quadradix
0.0002593361
Quay Park Medical Centre
0.0002772387
Queens Academic Group
0.0002593361
Quest Integrity Group Ltd.
0.0002753304
Quigley and Watts Ltd.
0.0002507523
Quin Environmentals(NZ) Ltd.
0.0002545177
Quintessence Developments Ltd.
0.0002393490
Quit Group
0.0002843332
Radiata Pine Breeding Company
0.0002252760
Radio Spectrum Management
0.0002466700
Rakon Ltd.
0.0002593361
Rangiora New Life School
0.0002590003
Rape Prevention Education-Whakatu Mauri
0.0002762431
Rauawaawa Kaumatua Charitable Trust
0.0002759382
Raukatauri Music Therapy Centre
0.0002593361
Raukura Hauora O Tainui Trust
0.0002492522
Rayonier New Zealand Ltd
0.0002595380
Refugees as Survivors New Zealand
0.0002619859
Reid Construction Systems Ltd
0.0002685285
Renewable Energy
0.0002252760
Repromed
0.0002835271
Reserve Bank of New Zealand
0.0002701243
Resilient Organisations
0.0002685285
Resource Teacher: Learning and Behaviour
0.0002593361
Revolution Fibres Ltd
0.0002783964
Riccarton Rotary
1.0000000000
Risk Strategies Research and Consulting
0.0002399232
Rivuli Development
0.0002308936
RML Engineering
0.0002308403
Roche Products Limited
0.0002619859
Rockwell Automation
0.0002593361
Rolleston Veterinary Clinic
0.0002693966
Ropata Village Medical Centre
0.0002786291
Rotorua General Practice Group
0.0002754821
Rowe Davies Research Ltd
0.0002632272
Royal Australian and New Zealand College of Psychiatrists
0.0002593361
Royal Forest and Bird Protection Society of New Zealand
0.0002648305
Royal New Zealand College of General Practitioners
0.0002836879
Royal New Zealand Plunket Society
0.0002912056
Royal Society of New Zealand
0.0002820079
Ruaimoko Productions and Consultancy Ltd.
0.0002491901
Rumenz Ltd
0.0002603489
RuralLink
0.0002308403
[ reached getOption("max.print") -- omitted 511 entries ]plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos1 * 50)
top_10_clos1 <- tail(sort(clos1), 10)
# Вектор-топ 42 также будет единичным, а вот вектор-топ 43 уже нет
top_10_clos1 Reveal Infrastructure Ltd. Napier City Council RATO Natural Health Clinic
1 1 1
Stahlton Engineered Concrete Katipo Communications Workwise Employment Ltd.
1 1 1
Northpower New Zealand Stock Exchange Real Time Genomics
1 1 1
Rotary Club of Riccarton
1 bottom_10_clos1 <- head(sort(clos1), 10)
bottom_10_clos1 Tauranga City Council
0.0001571092
Project Litefoot Trust
0.0001703868
Dumpark Data Science
0.0001706193
Dairy Production Systems Ltd.
0.0001720282
SciCon Scientific Consultants
0.0001725923
New Zealand Employment Service and Work and Income New Zealand
0.0001773050
IWM Consultancy
0.0001779676
PLANTwise Services Ltd
0.0001779676
Care of Orca Research Trust
0.0001794044
Southern Veterinary Centre
0.0001818843 clos1["University of Auckland"]University of Auckland
0.0004175365 clos2 <- closeness(net)
clos2 45 South Management Ltd.
0.0003943799
Abacus ALS
0.0003948148
AbacusBio Ltd.
0.0006961899
ABB Power Quality
0.0006413412
ABI Rehabilitation New Zealand Ltd.
0.0003938669
AC Research Associates
0.0005551376
Academic Colleges Group New Zealand
0.0005551376
Accident Compensation Corporation
0.0007801036
Action on Smoking and Health New Zealand
0.0007336460
Active Health
0.0003948964
Acurity Health Group ltd.
0.0008104601
Ade Consultants
0.0003949673
Adidas Sports Medicine
0.0005551376
Adis International Ltd.
0.0006422174
Advanced Clinical Skills Centre
0.0003949738
AECOM
0.0005553066
AECS Ltd.
0.0003939742
Aerocool Ltd.
0.0005531777
Aeroqual Ltd.
0.0006964490
Affinity Services
0.0003949673
AFT Pharmaceuticals Ltd
0.0006421838
AFTpharmaceuticals
0.0003949673
Agencies for Nutrition Action
0.0003950001
Agile Utilities New Zealand Ltd
0.0003947654
Agknowledge Ltd.
0.0003942829
AgResearch
0.0009296380
Agri-Optic NZ Ltd.
0.0003947654
Agribusiness Group
0.0003948792
AgriGenesis Biosciences Ltd
0.0003944997
AgriHealth NZ Limited
0.0005811195
Agrimm Technologies Ltd
0.0006911531
AgriNova NZ Ltd
0.0005536711
AgriQuality Limited
0.0005536711
Agvance Marketing Ltd.
0.0005548064
Air New Zealand
0.0007336460
Air Quality Ltd.
0.0003950063
Airborne Honey Ltd.
0.0003949205
Akaroa Medical Centre
0.0003948441
Ako Aotearoa National Centre for Tertiary Teaching Excellence
0.0006951944
Akoranga Integrated Health Clinic
0.0003945848
Alan Bell and Associates
0.0003897638
Albany Basin Accident and Medical Centre
0.0003935895
Alcohol Advisory Council of New Zealand
0.0003867563
Alcohol Harm Minimisation Advisory Group
0.0007321787
Alcohol Healthwatch Trust
0.0003949673
Alexandra Lions Club
0.0003936698
Alexandra Medical Centre
0.0003948441
Alfriston College
0.0003939742
All Seasons Pharmacy
0.0003949673
Allan Planning and Research Ltd.
0.0003934603
Allen & Clarke Policy and Regulatory Specialists Limited
0.0005550492
Alphalabs
0.0003942276
Alpine and Polar Processes Consultancy
0.0003948315
Alzheimers Northland
1.0000000000
Amalgamates Solutions and Research Ltd.
0.0005533577
Amity Health Centre
0.0003948441
Ancare New Zealand Ltd.
0.0005548944
Ancare Scientific Ltd
0.0007609563
Anexa FVC
0.0008104933
Anglesea Medical Properties Ltd
0.0005532196
Animal Dermatology NZ
0.0003944603
Animal Health Board New Zealand
0.0005538036
Animals and Marine Surveillance and Investigation Team
0.0003947654
Animation Research Limited
0.0003948441
Antarctic Heritage Trust
0.0003939742
Antarctica New Zelaand
0.0005532774
Antarctica Scientific Limited
0.0003937421
Antipodean Pharmaceuticals
0.0003948640
Aorangi Veterinary Services
0.0003782167
Aotea Pathology Ltd.
0.0007333288
Aotearoa Alcohol and Other Drug Consumer Network
0.0005553704
AP EnerTec Ltd.
1.0000000000
Applied Engineering Research Ltd.
0.0003896193
Applied Research and Technologies Ltd.
0.0004701219
Applied Research Associates New Zealand
0.0003937088
AquaBio Consultants Ltd.
0.0005460494
Aquaculture New Zealand
0.0006274107
Aqualinc Research Ltd.
0.0007917378
Aquanet Consulting Ltd.
0.0003947654
Aquatic Research Solutions Ltd.
0.0006379371
Aranui High School
0.0003937473
ARANZ Geo Ltd
0.0003937088
ARANZ Medical Scanning
0.0005547135
Areograph Ltd.
0.0007600330
ARH Construction
0.0003949673
Aroa Biosurgery
0.0006413752
Arohanui Hospice
0.0006666201
Arotec Diagnostics Ltd.
0.0005536524
Ascot Angiography
0.0003947988
Ascot Women's Cancer Centre of New Zealand
0.0003734750
Asia New Zealand Foundation
0.0003951218
Asphalt Products Limited
0.0005547135
Aspiring Veterinary Service Ltd
0.0003951294
ASR Limited Martine Consulting and Research
0.0003942151
Assa Abloy New Zealand Ltd
0.0003948441
Assistive Technology Ltd.
0.0003947654
Assurity Consulting Ltd
0.0005543822
AsureQuality
0.0003949212
AsureQuality Ltd.
0.0007970684
At the Vets
0.0005226062
Atkinson and Rapley Consulting
0.0005547389
Atlantis HealthCare
0.0003949673
Auckland-Waikato Fish and Game Council
0.0003946024
Auckland Astronomical Society
0.0003950014
Auckland Botanic Gardens
0.0003950034
Auckland Breast Centre
0.0003935895
Auckland City Mission
0.0003950891
Auckland Clinical Studies Ltd.
0.0003953194
Auckland Council
0.0008874012
Auckland Cricket Assn Inc
0.0003945848
Auckland Dermatology
0.0003938669
Auckland District Health Board
0.0009326414
Auckland Eye
0.0003950182
Auckland Heart Group
0.0006413449
Auckland Institute of Studies
0.0003946231
Auckland International Airport Limited
0.0003945848
Auckland Museum
0.0008683322
Auckland Refugee Community Coalition
0.0003949673
Auckland Regional Council
0.0003949673
Auckland Southern Cross Hospital Group
0.0007815128
Auckland Transport
0.0003949673
Auckland Zoo
0.0007292915
Aurecon
0.0007607093
Australian and New Zealand College of Anaesthetists
0.0005551376
AUT University
0.0009316976
Automation Design Ltd
0.0003823478
Aviation Industry Association of New Zealand Inc
1.0000000000
Avivet Ltd
0.0005547389
Avocado Industry Council
0.0003942244
Babbage Consulting Ltd.
0.0006415123
Ballance Agri-Nutrients Limited
0.0007605800
Bank of Scotland
0.0003949673
Bartonk Solutions
0.0005525811
Batten Animal Research Network
0.0005548944
Baxter Healthcare Limited
0.0005551376
Bay Audiology
0.0006413412
Bay of Plenty District Health Board
0.0008771219
Bay of Plenty Polytechnic
0.0008292245
Bay of Plenty Regional Council
0.0007937374
Bay Urology
0.0003947619
Bayer CropScience New Zealand
0.0003932645
Bayleys Property Services
0.0003949673
BC Consulting Ltd.
0.0007916542
BCRL Energy Limited
0.0003682590
Beca
0.0007985413
Beef and Lamb New Zealand
0.0003952621
Bennett Scientific
0.0005548944
Benthic Science Ltd.
0.0005548944
Berryworld Ltd
0.0005538244
Best Practice Advocacy Centre
0.0007810309
Beta Solutions
0.0003950277
Bethesda Care
0.0005551376
Betta Bees Research Ltd
0.0003948441
Better Border Biosecurity
0.0003942993
BHU Future Farming Centre
0.0003948009
Bickler Consultants Ltd.
0.0006419082
BikeNZ
0.0003947526
Bio Soil and Crop Ltd
1.2000000000
Bioactives Research New Zealand
0.0007980255
Biodiscovery New Zealand Ltd.
0.0007608293
Biomarine Ltd.
0.0003949673
Biomatters Ltd.
0.0005551376
Biometrics Matters Ltd
0.0006940374
Biopolymer Network Ltd
0.0006965300
Biosecurity New Zealand
0.0003949899
BioSylve Forest Science NZ Ltd.
0.0003896193
BirdLife Global Seabird Programme
0.0003895611
Blind Foundation
0.0003947654
BLIS Technologies Ltd.
0.0007603725
Blue Water Marine Research
0.0003949933
Blues Rugby Club
2.0000000000
Bodeker Scientific
0.0008045790
Body Aid Clinic Ltd
0.0003948441
Boffa Miskell Ltd
0.0006960747
Bomac Laboratories Ltd
0.0005552922
Boulcott Hospital
0.0003910446
Braemar Hospital
0.0003950591
BRANZ Ltd.
0.0008598606
Bream Bay Medical Centre
0.0003949673
Breast Care and Screening Services
0.0003949726
Breast Surgeons' Society of New Zealand
0.0003949673
Breen Consulting
0.0003935938
Brian Ricketts Geological Consulting Limited
0.0003936600
Broadway Medical Centre
0.0003949728
Broadway Surgical Clinic
0.0003942850
Broken Hills Gold Co
0.0003949673
Brownrigg Agriculture
0.0005444194
Bruce Shallard and Associates
1.0000000000
Bunnythorpe School
0.0003936698
Cadwallader Tree Consultancy
0.0003947526
Cahill Animal Hospital
0.0006413752
CAL Engineering Management
0.0005534681
Callaghan Innovation
0.0009254060
Cambridge Clinic
0.0003948798
Cambridge Veterinary Services
0.0003944603
Cameron Medical Clinic
0.0006357888
Campbell and Associates Ltd.
0.0003942244
Cancer Control Council of New Zealand
0.0003950238
Cancer Society of New Zealand
0.0005552162
Canterbury Charity Hospital Trust
0.0006418575
Canterbury Civil Defence and Emergency Management Group
0.0003947495
Canterbury District Health Board
0.0009314570
Canterbury Earthquake Recovery Authority
0.0005548674
Canterbury Health Ltd
0.0003950486
Canterbury Medical Imaging
0.0005518436
Canterbury Museum
0.0008831092
Canterbury Rugby Football Union and Crusaders
0.0003933134
CanZealand Geoscience Ltd
0.0003936626
Cape Kidnappers and Ocean Beach Wildlife Preserve
0.0003951234
Cape Sanctuary
0.0003950172
Capital and Coast District Health Board
0.0009276277
Capital Eye Specialists
0.0007298105
Capital Research
0.0003948493
Carbon Partnership
0.0003936698
Cardiac Inherited Disease Group
0.0003949738
Care of Orca Research Trust
0.0003311825
Carey Baptist College
0.0003949673
Carroll Consulting ltd
0.0003947798
Carson Associates Ltd.
0.0003896193
Carter Holt Harvey Ltd.
0.0005566828
Carter National Observatory
0.0005196524
Cashmere Health
0.0005550483
Catch Ltd.
0.0003949673
Catmed
0.0003931993
Cawthron Institute
0.0009084004
CBG Health Research Limited
0.0005551376
Centennial Health
0.0003951562
Center for Backyard Astrophysics
0.0006096491
Central and Southern New Zealand Craniofacial Program
0.0005474301
Central City Vets
0.0006413752
Central Otago Tourism
0.0003948441
Central Stories Museum
0.0006384881
CentralMed
0.0005504286
Centre for Backyard Astrophysics
0.0008956521
Centre for Clinical Research and Effective Practice
0.0006408984
Centre for Dairy Excellence
0.0003949213
Centre for Minerals Environmental Research (CMER)
0.0003948837
Centre for Research Evaluation and Social Assessment
0.0003812459
Centre for Youth Health in South Auckland
0.0005551376
CH and Associates
0.0006384881
ChangeMakers Refugee Forum
1.0000000000
Chatham Rock Phosphate Ltd.
1.0000000000
Chemipreneur Ltd.
0.0006279010
Chemistry Communications
0.0005551376
Chiefs Super Rugby Franchise
0.0003948667
Child and Youth Health
0.0005551376
Child Poverty Action Group
0.0003949673
Chilton Saint James School
1.0000000000
Chiptech Ltd
0.0003950001
Christchurch City Council
0.0008378900
Christchurch Emergency Care Foundation
0.0005542970
Christchurch Polytechnic Institute of Technology
0.0008922581
Christchurch Psychologists' Office
0.0003948909
Christchurch Vascular Group
0.0005548944
City Care Ltd
0.0003947526
City Fitness
0.0003949458
Civil Aviation Authority
0.0005552570
Claro
0.0003949673
ClearSight Consultants Ltd
0.0003951789
Clement and Associates Ltd
0.0003938701
Clendon Burns and Park Consulting Engineers
0.0003938581
CLIMsystems Ltd.
0.0005531777
Clinical Horizons
0.0003950194
Clinical Systems
0.0003942294
Clutha Veterinary Association
0.0003949337
Coast and Catchment Ltd
0.0005556945
Coast to Coast Health Centre
0.0003935895
Coastal and Aquatic Systems Ltd
0.0003955727
Coastal Systems (NZ) Ltd.
0.0003454406
Coastline Consultants
0.0003896193
Cognition Education Limited
0.0006419082
Cognosco
0.0006413752
Colgate-Palmolive Ltd
0.0003947526
Colin Christian Ltd.
0.0003948441
Collins Carriers Ltd.
0.0003932970
Colmar Brunton
0.0003949673
Columba College
0.0003948441
Common Ground Ltd
0.0006384881
Commtest Instruments Ltd
0.0003947526
Community Clinic for Sexual Health and Contraception
0.0003949673
Compac Sorting Equipment Ltd.
0.0003949932
Compac Technologies
0.0003947654
Compass Health
0.0005548944
Compusoft Engineering Limited
0.0003949673
Compusoft Engineering Ltd.
0.0005552917
Comtel System Ltd.
0.0003947832
Comvita New Zealand Ltd.
0.0007977788
Connectos Consulting
0.0003952960
Connovation Ltd.
0.0008146590
Conservation and Environmental Management
0.0003947613
Construction Techniques Ltd.
0.0003949990
Consulting Dietitians Ltd.
0.0005551376
Contact Energy Ltd.
0.0007818697
Contract Landscapes Ltd
0.0003454406
CORE Education Ltd.
0.0006392891
Cosgrove
0.0003947526
Counties Manukau District Health Board
0.0009297184
Covec Ltd
0.0005518436
CPG New Zealand Ltd.
0.0003947654
Crawford Medical Centre
0.0005552917
CRL Energy Ltd.
0.0007971428
Cromwell College
0.0003946024
Cropmark Seeds Limited
0.0005519960
Crown Fibre Holdings Limited
1.0000000000
CURT St George's Medical Centre
0.0003952228
Cuttriss Consultants Ltd
0.0003936626
Cymbiotix Group Limited
0.0003949837
Cyperus Ltd
0.0005551376
Dairy Consultants Ltd.
0.0003711287
Dairy Goat Co-operative (NZ) Ltd.
0.0006416496
Dairy Production Systems Ltd.
0.0002502698
DairyNZ
0.0009005769
David Butler Associates Ltd
0.0003947654
Davidson Environmental Ltd.
0.0003954379
DaVinci Clinic
0.0003239384
DCM Process Control Ltd.
0.0003949673
DEA Research Software Surgery Ltd.
0.0003949673
Deepwater Group Ltd
0.0003938701
DeerNZ
0.0003942244
Deloitte
0.0003950949
Department of Conservation
0.0009210028
Department of Corrections
0.0003947526
Development Action
0.0003946024
Development By Design
0.0003946024
Devon Medical Centre
0.0003855266
DHI Water and Environment
0.0003770065
Diabetes Otago Inc
0.0003948441
Diagnostic Laboratory
0.0005551376
Diagnostic Medlab
0.0007981768
Digestive Health Services
0.0003948510
Digital Sensing Limited
0.0006419986
Disability Connect
0.0003951234
Disability Resource Centre
0.0003952960
Diversity NZ
0.0003952960
DM Consultants
0.0005547982
DNA Investments Ltd.
0.0003894305
Dnature diagnostics and research Ltd.
0.0005548977
Doctors for Sexual Abuse Care
0.0006956650
Donaghys Industries
0.0003943799
Donald Beasley Institute
0.0007603725
Dorothy-Jean and Associates
0.0003931099
Dovedale Ltd.
0.0005547389
Downer EDI Works Limited
0.0003933422
Dr. Malcolm McKellar Ltd.
0.0003708396
Dragonfly Ltd.
0.0006896795
Drummond Food Science Advisory Ltd.
0.0003948441
Dumpark Data Science
0.0002501171
Duncan Cotterill
0.0005551511
Dunedin City Council
0.0003948469
Dunedin Heat Pumps Limited
0.0003948441
Dunedin South Veterinary Clinic
0.0003947654
Dunning Thornton Consultants Ltd.
0.0003951234
Dynamic Controls Ltd.
0.0006956607
Dynatest
0.0003951624
Dyspraxia Support Group of New Zealand
0.0003948510
Earthquake Commission
0.0005547135
Earthtech Consulting Limited
0.0003951234
Eastern Institute of Technology
0.0008434570
Eastern Region Fish and Game
0.0006392891
Eastern Suburbs Association Football Club (ESAFC)
0.0003950277
Eastland Veterinary Services Ltd.
0.0003948508
Eaton Power Quality Ltd.
0.0006956607
ECG Consultants
0.0003947654
Eco-Vista Photography and Research Ltd.
0.0005554535
Eco Nomos Ltd.
0.0003942629
Eco Research Associates Ltd
0.0006300524
ECoast Limited
0.0003941466
EcoGecko Consultants Ltd.
0.0005548944
Ecosynergy Group Ltd (EGL)
0.0003946024
Ectus Ltd
0.0003939742
Edmund Lawler and Associates Limited
0.0003946024
Education House
1.0000000000
Education Review Office
0.0003949673
Educational Leadership Project
0.0003939742
Electricity Authority
0.0006409449
Eli Lilly and Company (New Zealand) Limited
0.0003950671
Elmwood Orthopaedics
0.0003950001
Eltham District Veterinary Services
0.0005548415
Endoscopy Auckland
0.0003949737
Energy Efficiency and Conservation Authority
0.0006410819
Energy Solution Providers Ltd.
0.0003932970
EnForm Tech
0.0003936799
Enigma Publishing Ltd.
0.0003949858
Ensys Ltd
0.0005547135
Entecol Ltd.
0.0006419082
Enviro-Mark Solutions Ltd.
0.0003947526
Enviro Research
0.0003943704
Environment Canterbury
0.0008329125
Environment Protection Authority(EPA)
0.0005536524
Environmental Management Services
0.0003936626
Environmental Restoration Ltd
0.0003896193
ENZO Nutraceuticals Limited
0.0003948901
Epi-interactive
0.0006413752
Epsom Girls Grammar School
0.0005551376
Equine Health Association
0.0003894305
ERA Ecology
0.0003951517
Erin Park
0.0005551376
ESR
0.0009235163
Etec Crop Solutions
0.0003942244
Eudyptes EcoConsulting Ltd
0.0003948690
Explore NZ
0.0003947654
Eye Institute
0.0003949738
Far North District Council
0.0003952353
Farm Cove Observatory
0.0008670861
Feilding Medical Centre
0.0003951299
FEM Ltd.
1.0000000000
Fern Research Foundation
0.0005383698
Ferndale School
0.0003947526
Fertility Associates
0.0007815128
Financial Markets Authority
0.0003946024
Fish and Game NZ
0.0006923050
Fisher and Paykel Appliances
0.0003949673
Fisher and Paykel Healthcare Ltd.
0.0006414556
Fishing Vessel Management Services Ltd.
0.0006360855
FitzRoy of Merivale
0.0003948069
Fletcher Construction Co
0.0003953577
FMR GROUP LTD
0.0005536711
Fonterra
0.0009190213
Food and Bio-based Products Group
0.0006399482
Food and Health Group
0.0005547389
Foot Science International Ltd.
0.0003948441
Forensic and Industrial Science Ltd
0.0005551376
Forest and Bird
0.0005547389
Forever Beech Ltd.
0.0003947526
Foundation for Arable Research
0.0006949293
Foundation for Research Science and Technology
0.0003947654
Fox and Associates-Consulting Surveyors
0.0003947901
Fred Hollows Foundation
0.0008866528
Fresenius Medical Care Australia Pty Ltd (New Zealand Branch)
0.0003949728
Freshport NZ Ltd
0.0003932970
Frontier Global Ltd.
0.0003949673
Fruitfed Supplies
0.0006402214
Fruition Horticulture
0.0007310869
FullSpectrum Ltd.
0.0003939742
Fulton Hogan Ltd.
0.0006967793
Future Forests Research
0.0003896193
Future Steps
0.0003950367
FuturebyDesign Ltd.
0.0003951613
FutureMATH Ltd.
0.0003647701
Gallagher Animal Management Systems
0.0003939742
Gambling Helpline
0.0003947959
Genesis Research & Development Corporation Ltd
0.0007608293
Genetic Technologies Ltd.
0.0005547389
Gentrack Limited
0.0003946543
Geoenvironmetal Services
0.0003711999
GEOKEM
0.0005271858
Geomarine Research
0.0008326418
Geoscience Consulting Ltd
0.0003949673
Geotech Consulting Ltd
0.0005529281
Geothermal Engineering Ltd
0.0003949673
Geoventures Limited
0.0003948441
GF McLaren Research Limited
0.0003943799
GHD Centre Level Napier St.
0.0003949673
GHD Limited
1.0000000000
Gillies McIndoe Research Institute
0.0008707798
Gisborne District Council
0.0003938581
Glass Earth Gold Ltd
0.0003948441
Glenview Medical Centre
0.0005551382
Global Action for Health Equity Network (HealthGAEN)
0.0005547389
Global Public Health Company Ltd
0.0007336460
GNS Science
0.0009265722
Golden Bay Cement
0.0003950453
Golder Associates (NZ) Ltd
0.0005555916
Good Life Research Centre Trust
0.0005643713
Google
0.0003946024
Greater Wellington Regional Council
0.0006410844
Green Lane Hospital
0.0005524197
Greenweaver Architecture Ltd
0.0003946535
Greerton Early Childhood Centre
0.0003948140
Gribbles Veterinary
0.0008453181
GroPlus Ltd.
1.5000000000
Ground Investigation Ltd
0.0003949673
Growth Solutionz
1.0000000000
Guardian Health Care (Bupa)
0.0005551376
Hagley Community College
0.0003947526
Hally Labels
0.0005544170
Hamilton Eye Clinic
0.0003949673
Hamilton Sacred Heart College for Girls
0.0003939742
Hamilton Veterinary Services
0.0003947654
Hamilton Zoo
0.0005505780
Hanham Consultants
0.0003949673
Hanmer Clinic Tauranga
0.0003948441
Hapai Te Hauora Tapui Ltd
0.0005551376
Harker Underground Construction Limited
0.0003949085
Harris Consulting
0.0003942843
Hauora Heretaunga
0.0005551376
Hauora Waikato Group
0.0007336460
Hauraki Maori Trust Board
0.0003949725
Hawke's Bay Alcohol and Drug Service
0.0003951135
Hawke's Bay District Health Board
0.0008313328
Hawke's Bay Regional Council
0.0003957986
Hawkins Watts
0.0003949673
Health Alliance
0.0003949710
Health Care Aotearoa
0.0003947526
Health New Zealand Ltd.
0.0008605536
Health Outcomes Associates Ltd.
0.0006963278
Health Partners Consulting Group
0.0008109060
Health Promotion Agency
0.0008213924
Health Quality and Safety Commission
0.0008109797
Healthscope Laboratories
0.0003682943
HealthWEST
0.0006963278
Heart Foundation of New Zealand
0.0006963278
Heavy Engineering Research Association
0.0006420456
HEB Construction
0.0003604172
Heinz Wattie's
0.0003949285
Heke Consulting
0.0003949673
Helios Integrative Medical Centre
1.0000000000
Hemptech
0.0007302269
Henderson Medical Centre
0.0003950176
Henderson Valley Primary School
0.0005531777
Hepatitis Foundation of New Zealand
0.0007816001
Herbert Morton Accountants
0.0003939742
Heretaunga Health
0.0003949738
Heritage New Zealand Pouhere Taonga
0.0003949673
High Performance Sport New Zealand
0.0008775866
Highnam Associates Ltd.
0.0003949673
Hill Laboratories Ltd.
0.0006932469
Hiway Geotechnical
0.0003949673
HodderBalog Social and Scientific Research
0.0003946024
Holcim (NZ)
1.0000000000
Holmes Consulting Group
0.0008103147
Holmes Fire and Safety
0.0005547135
Horizons Regional Council
0.0005539428
Horowhenua Community Practice
0.0003948441
Horowhenua Library Trust
1.0000000000
Horteye Ltd
0.0003943021
HortPlus
0.0005541313
Hospice New Zealand
0.0005550486
Hospice Palliative Care Education
0.0003949290
Hospice Waikato
0.0005543828
Hot Solutions Ltd.
0.0005551376
Humes Pipeline Systems
0.0003949673
Huntly Community Link
1.0000000000
Hurricanes Rugby
0.0003946322
Hush Interiors Ltd
0.0003947526
Hutt Valley District Health Board
0.0009121981
Hyland Consultants
0.0003940438
Hyland Fatigue Earthquake Engineering
0.0003955350
Hyperbaric Health
0.0005551505
IAG
0.0003947526
Ian Kusabs and Associates Limited
0.0005532740
Ian McLean Consultancy Services Ltd.
0.0003949673
Ichthyo-niche
0.0003949158
IGENZ Ltd
0.0006957865
ILR
0.0006418575
Immunisation Advisory Centre
0.0005551376
Inclusive Education Action Group
0.0003951234
Independent Petroleum Laboratory
0.0003949932
Indufor Asia-Pacific Ltd
0.0007764079
Infoics Limited
0.0005536524
Inform Planning Ltd
0.0003951701
Infrastructure Decisions Limited
0.0003949059
Inglewood Veterinary Services
0.0003947713
Injury Prevention Aotearoa
0.0003949903
Inland Revenue
0.0003946902
Innate Immunotherapeutics Limited
0.0005484222
Innate therapeutics
0.0003946024
Inner City Women's Group
0.0003949673
Inner Zest Ltd.
0.0003949673
INR Online Ltd
0.0003855266
Insect Science Solutions
0.0003943162
Insights MSD
0.0003708776
Inspiring Ltd.
0.0005552162
Institution of Professional Engineers New Zealand
0.0003949879
Intellectual Property Office of New Zealand
0.0003944997
Intensive Care Flight Paramedic
0.0003948291
Interactionz
0.0003939742
InterAg
0.0005538070
International Animal Welfare Consultants Limited
0.0003947654
International Earth Sciences IESE Ltd.
0.0003950220
International Pacific College
0.0005547389
International Student Ministries of New Zealand
0.0003950001
International Telematics Ltd.
0.0003947995
Interpine
0.0005447663
Interpine Forestry Ltd
0.0005450014
Intus Digestive and Colorectal Care
0.0003948441
Invenco Group Ltd.
0.0005551376
Investigation Geology Ltd
0.0003949085
IPENZ
0.0005551376
Irrigation New Zealand Inc.
0.0003944594
Isolytix
0.0003948441
IZON Science Ltd.
0.0007324195
Jackett Consulting
0.0003780628
Jacobs Engineering
0.0003953577
Jade Software Corporation
0.0003948909
James and Monroe
0.0003947959
JMR Distributors Ltd
0.0005547389
John Jones Steel
0.0003951551
John Wood Consulting
0.0003950740
Johne's Management Limited
0.0003948525
Jowett Consulting Ltd.
0.0003936120
JRA (NZ) Ltd.
0.0005551376
Julian King and Associates Limited
0.0003947667
Ka Mau Te Wero
0.0003936698
Kaikorai Valley College
0.0003948441
Kaikoura Ocean Research Institute Inc.
0.0003949911
Kaipaki Veterinary Services
0.0003947654
Kaipara District Council
0.0003952353
Kapiti Coast District Council
0.0003949825
Karori Sanctuary Trust
0.0006358197
Katoa Ltd
0.0005553001
Kea Conservation Trust
0.0003937253
KEA Consultant
1.0000000000
Keratec Ltd.
0.0005550207
Kidney Health New Zealand
0.0006419082
Kina Families and Addictions Trust
0.0003949696
Kinetic Engineering Design
0.0003949673
Kingdom Clinic
0.0003950354
Kiwi Well Evaluation Ltd
0.0003948935
Kiwi Wildlife
0.0005383698
Kiwicap Research Ltd
1.0000000000
Kiwikiwi Research and Evaluation Services
0.0003712462
Kono Horticulture Limited
0.0003948792
Koru Environmental Consultants Ltd
0.0003934932
Koti Technologies
0.0005547135
Kumeu Observatory
0.0008956520
Kurahaupo Consulting
0.0005525778
KVB Kunlun New Zealand Limited
0.0005547389
Labtests
0.0008219931
Lake Hawea Institute of Cryodynamics
0.0003948107
Lakes District Health Board
0.0007816012
Land Information New Zealand
0.0006416779
Landcare Research
0.0009266123
Landcorp Farming Limited
0.0005536524
Langimalie Clinic
0.0003947896
LanzaTech NZ Ltd.
0.0003949479
Lassey Research and Education Ltd
0.0003934603
Lateral Technology
0.0003949673
Laura Fergusson Trust
0.0005542970
Law Commission
0.0003946024
LeaderBrand Produce Ltd.
0.0003942762
Learning for Sustainability
0.0008251320
Leather & Shoe Research Association of New Zealand
0.0008550299
Leinster Orthopaedic Centre
0.0003780896
Levare Limited
0.0005551376
Levin and Horowhenua Veterinary Centre
0.0003947722
Lewis and Barrow Ltd.
0.0005534681
LIC
0.0008265458
Life Technologies Ltd.
0.0003947526
LightBox Psychology Services
0.0003948909
Lincoln Agritech Ltd.
0.0008662359
Lincoln University
0.0009245498
Lincolne Scott Ltd.
0.0003947526
Lindis Consulting
0.0005519960
Linnaeus Laboratory
0.0003948059
Litmus
0.0005552917
Livestock Solutions and Services
0.0005547389
Living Cell Technologies NZ Ltd.
0.0006419082
Local Government New Zealand
0.0003950950
Logjiztix Ltd
0.0003452421
Lowe NZ
0.0003934603
Lucas Industries (NZ) Ltd.
0.0003949673
LWT Animal Nutrition Ltd.
0.0006413752
MacMurray Hypertension Clinic Ltd
0.0003949781
MAGAK
0.0003936600
Magic Sparks Early Learning and Development Centre
0.0003950496
Magritek Limited
0.0007594764
Makoura College
0.0003946024
Malaghan Institute of Medical Research
0.0009149861
Male Survivors of Sexual Abuse Trust
0.0003947526
Manaaki Te Awanui
0.0003950746
Manaia Health Primary Health Organisation
0.0003945996
Manawatu Diagnostics
0.0005547389
Mangere Community Health Trust (Primary Health Organisation)
0.0006419082
Manukau Institute of Technology
0.0008513518
Manukau SuperClinic
0.0005551376
Manurewa South School
0.0003949673
Maori Hill Clinic
0.0003948441
Maori Pharmacists Association
0.0007336460
Maramatanga Consultants Ltd
0.0003947654
Marine Fisheries Research Services Limited
0.0005514962
Marine Wildlife Research Ltd
0.0005551847
Marinoto Clinic
0.0005548960
Mark L Batchelar Consulting Engineers
0.0003947526
Market Economics Ltd.
0.0007329499
Marlborough Wine Research Center
0.0007786096
MARS Bioimaging Ltd
0.0007335081
Marshall Day Acoustics Ltd.
0.0003950380
Mary Potter Hospice
0.0006957007
Massey University
0.0009327055
Masters Consulting Ltd.
0.0003931206
Matakina Technology Ltd
0.0005544170
Matamata Medical Centre
0.0003950247
Matamata Veterinary Services Ltd
0.0006959428
MBCentury Ltd
0.0003949673
McConnell Dowell Constructors Ltd.
0.0004890228
McLaren Research Ltd.
0.0003942244
McManus Geotech Ltd.
0.0003814080
Medical Council of New Zealand (MCNZ)
0.0003312818
Medical Research Institute of New Zealand
0.0009205848
Medlab Central
0.0003952279
Melanoma Unit
0.0006963278
Member International Neuropsychological Society
0.0003948441
Mental Health Education Resource Centre
0.0003947526
Mental Health Foundation of New Zealand
0.0006956650
MercyAscot Hospitals
0.0008844685
Meridian Energy Ltd.
0.0003948545
Mesynthes Ltd.
0.0005546049
Meteorological Service of New Zealand Ltd.
0.0006384751
Methanex
0.0005547389
MetOcean Solutions Ltd.
0.0005536407
Microfossil Research Ltd
0.0008110522
MidCentral District Health Board
0.0008811700
Midland MRI
0.0003939742
Midland Regional Forensic Services
0.0003949673
Midlands Health Network
0.0006420456
Midwifery Council of New Zealand
0.0003950778
Mighty River Power Ltd.
0.0007599517
Millar Instruments
0.0008217229
Milton Health Centre
0.0003951562
Ministry for Primary Industries
0.0009034630
Ministry for Primary Industry
0.0003949229
Ministry for the Environment
0.0007415055
Ministry of Business Innovation and Employment
0.0006956908
Ministry of Civil Defence and Emergency Management
0.0003937700
Ministry of Education
0.0006963410
Ministry of Foreign Affairs and Trade
0.0006959451
Ministry of Health
0.0009059174
Ministry of Justice
0.0003951252
Ministry of Pacific Island Affairs
0.0006963278
Ministry of Social Development
0.0003951315
Ministry of Transport
0.0003946784
Mission Heights Primary School
0.0005514962
MLB Consulting Engineers
0.0003947526
Molehill Astronomical Observatory
0.0008499141
Moorhouse Medical Clinic
0.0006951397
Morrison Consultants Ltd
0.0003750864
Motu Economic and Public Policy Research
0.0008664519
Mountains to Sea Conservation Trust
0.0003954054
MSD Animal Health Ltd
0.0006417868
Mt. Albert Psychological Services Ltd
0.0003795639
Mulgor Consulting Ltd.
0.0003940338
Muscular Dystrophy Association of New Zealand
0.0006413449
MWH New Zealand Ltd
0.0005552002
N-Squared Software
0.0005551376
NaeNae Medical Centre
0.0005529387
National Addiction Centre
0.0003948441
National Association of Steel-Framed Housing Inc
0.0005552403
National Council of Women of New Zealand
0.0005547925
National Heart Foundation of New Zealand
0.0008385590
National Library of New Zealand Te Puna Matauranga O Aotearoa
0.0006410819
National Maori Health Workforce Organisation
0.0003948441
Natural Resource Assessors
0.0003949254
Needle Exchange Programme NZ
0.0005553704
Nelson Forests Limited
0.0003948492
Nelson Marlborough District Health Board
0.0008639106
Nelson Marlborough Fish and Game
0.0005548944
Nelson Marlborough Institute of Technology
0.0006415830
Nelson Marlborough Regional Council
0.0006384881
Neonatal Intensive Care Unit
0.0005548944
NetSafe
0.0005551376
NetValue
1.0000000000
Neuren Pharmaceuticals
0.0003949673
Neurological Foundation of New Zealand
0.0005551376
New Brighton Health Care
0.0006418587
New Image Group Ltd
0.0005551376
New River Ltd
0.0003950001
New Zealand Academy of Sport
0.0006952606
New Zealand Aerial Mapping
0.0003950794
New Zealand Agricultural Greenhouse Gas Research Centre
0.0006939926
New Zealand Agriseeds Limited
0.0003947986
New Zealand AIDS Foundation
0.0008211901
New Zealand Aluminium Smelters Limited
0.0003949673
New Zealand Antarctic Institute
0.0003947526
New Zealand Arable
0.0005543189
New Zealand Association of Optometrists
0.0003948280
New Zealand Avocado Growers Association
0.0003942244
New Zealand BioSecure Entomology Laboratory Research
0.0005536524
New Zealand Blood Service
0.0008093342
New Zealand Brain Research Institute
0.0009150841
New Zealand Breast Cancer Foundation
0.0005542970
New Zealand Centre for Conservation Medicine (NZCCM)
0.0006959157
New Zealand Climate & Health Council
0.0003950071
New Zealand College of Chiropractic
0.0006408984
New Zealand College of Midwives
0.0007336612
New Zealand Cot Death Association
0.0003950453
New Zealand Council for Educational Research (NZCER)
0.0007329055
New Zealand Defence Force
0.0007810309
New Zealand Dental Association
0.0003949741
New Zealand Employment Service and Work and Income New Zealand
0.0002504864
New Zealand Familial Gastrointestinal Cancer Service
0.0005549996
New Zealand Forestry Ltd
0.0003897332
New Zealand Geotechnical Society Ine (NZGS)
0.5000000000
New Zealand Guidelines Group
0.0003950188
New Zealand Gynaecological Cancer Foundation
0.0003948835
New Zealand Heart and Lung Transplant Service
0.0005547162
New Zealand Heavy Engineering Research Association
0.0006963278
New Zealand Homebased Early Childhood Education Association
0.0003948619
New Zealand Institute for Plastic and Cosmetic Surgery
0.0003948441
New Zealand Institute of Community Health Care
0.0006410179
New Zealand Institute of Economic Research
0.0007333916
New Zealand Institute of Medical Laboratory Science
0.0005549207
New Zealand Institute of Rural Health
0.0003950071
New Zealand Kiwi Foundation
0.0003949673
New Zealand Medical Association
0.0005548944
New Zealand Medical Students' Association
0.0005548944
New Zealand National Eye Bank
0.0003950659
New Zealand National LCP Office
0.0003951792
New Zealand Needle Exchange Programme
0.0006421257
New Zealand Nurses Organisation
0.0005548944
New Zealand Olympic Committee
0.0003948441
New Zealand Organisation for Rare Disorders (NZORD)
0.0003948441
New Zealand Parliament
0.0003946024
New Zealand Police
0.0006905753
New Zealand Qualifications Authority
0.0003946024
New Zealand Refining Co. Ltd.
0.0003947526
New Zealand Rheumatology Association
0.0003950180
New Zealand Rugby Union
0.0007803645
New Zealand School Acupuncture and Traditional Chinese Medicine
0.0003947526
New Zealand School of Music
0.0007323880
New Zealand Seafood Industry Council Ltd
0.0006362204
New Zealand Society for Earthquake Engineering (NZSEE)
0.5000000000
New Zealand Spinal Trust
0.0006407846
New Zealand Tertiary College
0.0006963278
New Zealand Timberlands Ltd
0.0003650302
New Zealand Transport Agency
0.0007821668
New Zealand Treasury
0.0008095149
New Zealand Underwater Heritage Group
0.0003941294
New Zealand Veterinary Pathology Ltd.
0.0008806712
New Zealand Winegrowers
0.0003949933
Newman Energy Research
0.0003947526
Newtown Medical Centre
0.0003950071
NextWindow Ltd
0.0003950071
Ngati Porou Hauora
0.0005551376
Ngati Whakaue Tribal Lands Inc
0.0003896193
Nielsen Company
0.0005551379
NIU Development Incorporated
0.0005551376
NIWA
0.0009254523
Norske Skog Tasman
0.0003949673
North Canterbury Veterinary Clinics
0.0003951629
North Shore Hospice
0.0005551701
North Shore International Academy
0.0003948283
Northcott Research Consultants Ltd.
0.0006416218
Northern Cancer Network
0.0006419082
Northern Region IDEA Services
0.0003949673
Northern Regional Alliance
0.0005524197
Northern Southland Veterinary Services
0.0003785031
Northland District Health Board
0.0008112734
Northland Regional Council
0.0003959682
NorthTec
0.0006413752
Novare Design Ltd.
0.0003947526
Numcore Ltd.
0.0003949673
Numinos Ltd.
0.0003949673
Nurse Maude Association
0.0007323038
Nutrigenomics New Zealand
0.0008109060
Nutrition Society of New Zealand
0.0005548944
NZ Oil and Gas
0.0003946252
NZ Parsa Tiling Limited
0.0003947526
NZFOCUS (NZ) Ltd.
0.0005551376
NZX Limited
0.0003949673
O'Kane Consultants (NZ) Ltd
0.0003950448
Oamaru Hospital
0.0005548944
Odyssey House
0.0005551376
Office of the Health and Disability Commissioner
0.0003949673
Office of the Parliamentary Commissioner for the Environment
0.0006415830
Omahu Urology Clinic
0.0003948493
OMV New Zealand Ltd.
0.0005544620
Oncology Surgery Ltd.
0.0005551376
Open Polytechnic of New Zealand
0.0008094440
OPRA Consulting Group
0.0003950645
Optimal Clinical Trials
0.0005550608
Opus International Consultants Ltd
0.0008445494
Oracle New Zealand
0.0003946024
Oral Health Centre
0.0003948575
Orange Consulting
0.0003948441
Orb Solutions
0.0003949487
Organ Donation New Zealand
0.0006419082
Oritain Global Ltd.
0.0003948441
Ornithological Society of New Zealand
0.0003949882
Orokonui Ecosanctuary
0.0003948935
OSPRI
0.0006923050
Otago Community Hospice
0.0003948937
Otago Computational Modelling Group Ltd.
0.0006964497
Otago Daily Times Collective
0.0003948441
Otago Girls High School
0.0003950977
Otago Museum
0.0007332212
Otago Polytechnic
0.0009121691
Otago Regional Council
0.0006822045
Otahuhu College
0.0006419082
Otakaro Pathways Ltd
0.0003945937
Otorohanga Dental Surgery
0.0003948441
OTRS Group Ltd
0.0003949173
Outome Management Services
0.0003949673
P.N. Plimmer and Associ.
0.0003951234
PA Handford and Assoc. Ltd.
0.0003896489
Pacific Brands
0.0005551376
Pacific Edge Biotechnology Ltd.
0.0006419949
Pacific Health Research and Development Foundation
0.0005551376
Pacific Radiology Group
0.0008446833
Pacific Women's Health Research and Development Unit
0.0003949829
Pakuranga Medical Centre
0.0005536809
Palaecol Research Ltd
0.0008375333
Palmerston North City Council
0.0005548928
Palmerston North City Library
0.0003946024
Pansophy Ltd
0.0007764492
Papamoa Pines Medical Centre
0.0006890931
Paraparaumu College
0.0005551460
Paric Limited
0.0003949673
Parkinson's New Zealand
0.0005551376
Parresia Research Limited
0.0003949673
Parsons Brinckerhoff
0.0003949673
Pasifika Horizon Healthcare
0.0003949673
Pasifika Medical Association
0.0003950030
Pasifika Research Ltd
0.0005545713
Pathlab
0.0006150037
Patients First
0.0005548944
Paton-Simpson Associates Limited
0.0003948706
Pattle Delamore Partners Ltd
0.0003947917
Pegasus Health Ltd
0.0008091865
Penny and Associates Ltd
0.0005536809
Perinatal and Maternal Mortality Review Committee
0.0005551505
Petersgate Counselling Centre
0.0003947526
PF Olsen and Company Ltd
0.0005446303
PGG Wrightson Seeds Ltd.
0.0007313750
PHARMAC
0.0006964515
Pharmaceuticol Ltd
0.0003949784
Pharmacy Guild of New Zealand
0.0003949673
PharmTech Service Limited
0.0005553899
Philosophy of Education Society of Australasia
0.0003949673
Photonz Corporation Ltd
0.0003949673
Pictor Ltd.
0.0003949673
Pingar Research
0.0005533307
Pinnacle Group Ltd
0.0003950664
PipeTechnologies
0.0003953577
Pipfruit New Zealand
0.0005536711
Planning Consultants Ltd
0.0003951701
Plant and Food Research
0.0009296908
Plant Protection Chemistry NZ Ltd
0.0007160207
PlusGroup Limited
0.0005536881
Pohatu Penguins
0.0003943316
Polybatics Ltd.
0.0006413752
Porirua City Council
0.0003948441
Ports of Auckland Limited
0.0003951234
Positive Thinking Ltd
0.0005551376
Possum Observatory
0.0008907799
Potter Building Services Ltd.
0.0003950527
Power Co Ltd.
0.0003949673
Power Systems Consultants New Zealand Ltd
0.0005093034
PowerbyProxi Ltd.
0.0007336460
Powerhouse Ventures Ltd
0.0005547135
Practitioners First Limited
0.0003950455
Presbyterian Church of New Zealand
0.0003949738
PriceWaterhouse Coopers (PwC)
0.0006939926
Priestley Structural Engineering
0.0003950332
Private Endodontic Practice
0.0003948441
ProCare Health Limited
0.0006963278
Prohealth Physiotherapy Ltd
0.0005548944
Promisia Ltd
0.0003948963
Proteus Wildlife Research Consultants
0.0008281416
Psychological Service
0.0003949673
Psychology Centre
0.0005551376
Pultron Composites Ltd.
0.0007576096
Pyrotek
0.0006957817
Q-Bit Ltd.
0.0003948009
QE Health
0.0003949738
Qnique Ltd
0.0003950392
QStar Solutions Ltd.
0.0006956607
Quadradix
0.0003949673
Quay Park Medical Centre
0.0005547162
Queens Academic Group
0.0005551376
Quest Integrity Group Ltd.
0.0008573649
Quigley and Watts Ltd.
0.0005548944
Quin Environmentals(NZ) Ltd.
0.0003948961
Quintessence Developments Ltd.
0.0003949205
Quit Group
0.0008451921
Radiata Pine Breeding Company
0.0006798754
Radio Spectrum Management
0.0003948194
Rakon Ltd.
0.0006419082
Rangiora New Life School
0.0005547135
Rape Prevention Education-Whakatu Mauri
0.0006419082
Rauawaawa Kaumatua Charitable Trust
0.0003950124
Raukatauri Music Therapy Centre
0.0003949673
Raukura Hauora O Tainui Trust
0.0006960663
Rayonier New Zealand Ltd
0.0005551376
Refugees as Survivors New Zealand
0.0003949738
Reid Construction Systems Ltd
0.0006963278
Renewable Energy
0.0003896193
Repromed
0.0006413449
Reserve Bank of New Zealand
0.0007571528
Resilient Organisations
0.0006413412
Resource Teacher: Learning and Behaviour
0.0003949673
Revolution Fibres Ltd
0.0003950578
Riccarton Rotary
1.0000000000
Risk Strategies Research and Consulting
0.0007330129
Rivuli Development
0.0003940518
RML Engineering
0.0003939742
Roche Products Limited
0.0003949738
Rockwell Automation
0.0003949673
Rolleston Veterinary Clinic
0.0003950567
Ropata Village Medical Centre
0.0006419231
Rotorua General Practice Group
0.0003950071
Rowe Davies Research Ltd
0.0006408984
Royal Australian and New Zealand College of Psychiatrists
0.0003949673
Royal Forest and Bird Protection Society of New Zealand
0.0006963278
Royal New Zealand College of General Practitioners
0.0007336460
Royal New Zealand Plunket Society
0.0006955571
Royal Society of New Zealand
0.0003950578
Ruaimoko Productions and Consultancy Ltd.
0.0005548944
Rumenz Ltd
0.0003949789
RuralLink
0.0003939742
[ reached getOption("max.print") -- omitted 511 entries ]plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos2 * 50)
top_10_clos2 <- tail(sort(clos2), 10)
top_10_clos2 Workwise Employment Ltd. Northpower New Zealand Stock Exchange
1.0 1.0 1.0
Real Time Genomics Rotary Club of Riccarton Bio Soil and Crop Ltd
1.0 1.0 1.2
PollenPlus Ltd. GroPlus Ltd. Blues Rugby Club
1.2 1.5 2.0
Highlanders Rugby
2.0 bottom_10_clos2 <- head(sort(clos2), 10)
bottom_10_clos2 Dumpark Data Science
0.0002501171
Dairy Production Systems Ltd.
0.0002502698
New Zealand Employment Service and Work and Income New Zealand
0.0002504864
Project Litefoot Trust
0.0002504870
Tauranga City Council
0.0002955979
Port Otago Ltd
0.0003060701
Travel Clinic
0.0003065386
Dobbie Engineers Ltd.
0.0003069975
NZ Strong Construction
0.0003069975
Pulp Mill Technical Group
0.0003069975 clos2["University of Auckland"]University of Auckland
0.0009338331 Вывод: В обоих случаях максимальная центральность
вершин будет составлять 1. В нашем графе существует 21 пара
вершин, которая связана лишь между собой и более ни с кем (из рассчета
для графа с единичными весами ребер). Из них лишь 5 организаций работали
совместно более 1 раза (из рассчета для графа с обратными весами).
Топ-10 центральных вершин по близости и топ-10 по степени уже
существенно различаются. Так, центральность по близости университета
Окленда составит 4.1753653^{-4} в первом случае и 4.1753653^{-4}. Т.е.
round(1 / clos1["University of Auckland"]) или
round(1 / clos2["University of Auckland"]) — сумма длин
всех путей от университета Окленда до любой другой вершины в зависимости
от метода рассчета.
Центральность по кратчайшему пути
betw1 <- betweenness(net, weights=NA)
head(betw1) 45 South Management Ltd. Abacus ALS
0.0000 0.0000
AbacusBio Ltd. ABB Power Quality
228.0179 0.0000
ABI Rehabilitation New Zealand Ltd. AC Research Associates
0.0000 0.0000 top_10_betw1 <- tail(sort(betw1), 10)
top_10_betw1 Auckland District Health Board Plant and Food Research AgResearch
44138.73 55148.49 61204.78
University of Waikato AUT University Victoria University of Wellington
62949.44 64866.37 84858.46
University of Canterbury Massey University University of Otago
130456.08 194334.96 231358.36
University of Auckland
385421.47 bottom_10_betw1 <- head(sort(betw1), 10)
bottom_10_betw1 45 South Management Ltd. Abacus ALS
0 0
ABB Power Quality ABI Rehabilitation New Zealand Ltd.
0 0
AC Research Associates Academic Colleges Group New Zealand
0 0
Action on Smoking and Health New Zealand Active Health
0 0
Ade Consultants Adidas Sports Medicine
0 0 betw1["University of Auckland"]University of Auckland
385421.5 betw2 <- betweenness(net)
head(betw2) 45 South Management Ltd. Abacus ALS
0 0
AbacusBio Ltd. ABB Power Quality
1 0
ABI Rehabilitation New Zealand Ltd. AC Research Associates
0 0 top_10_betw2 <- tail(sort(betw2), 10)
top_10_betw2 Auckland District Health Board Plant and Food Research AUT University
48988.50 57655.33 74583.33
University of Waikato AgResearch Victoria University of Wellington
81434.50 96575.50 139495.17
University of Canterbury Massey University University of Otago
198521.67 323919.17 340995.17
University of Auckland
815924.25 bottom_10_betw2 <- head(sort(betw2), 10)
bottom_10_betw2 45 South Management Ltd. Abacus ALS
0 0
ABB Power Quality ABI Rehabilitation New Zealand Ltd.
0 0
AC Research Associates Academic Colleges Group New Zealand
0 0
Accident Compensation Corporation Action on Smoking and Health New Zealand
0 0
Active Health Acurity Health Group ltd.
0 0 betw2["University of Auckland"]University of Auckland
815924.2 Вывод: При разных методах минимальные значения
центральности у вершин будут равны 0. Это вершины,
расположенные на периферии графа, или те, которые вовсе имеют всего
одного соседа (например, та 21 пара вершин). Максимальные центральности
вершин превышают 40 000 в топ-10. В обоих случаях
университет Окленда на первом месте (3.8542147^{5} и 8.1592425^{5}).
Значительное число кратчайших путей между любыми двумя вершинами
проходит именно через данный университет.
Центральность по собственному значению
eig1 <- eigen_centrality(net, weights = NA)
head(eig1)$vector
45 South Management Ltd.
0.0085447751
Abacus ALS
0.0225025837
AbacusBio Ltd.
0.0634333214
ABB Power Quality
0.0148191986
ABI Rehabilitation New Zealand Ltd.
0.0073868398
AC Research Associates
0.0424816145
Academic Colleges Group New Zealand
0.0249346566
Accident Compensation Corporation
0.1565499955
Action on Smoking and Health New Zealand
0.0249346566
Active Health
0.0221603845
Acurity Health Group ltd.
0.1302323254
Ade Consultants
0.0249346566
Adidas Sports Medicine
0.0249346566
Adis International Ltd.
0.0336599761
Advanced Clinical Skills Centre
0.0357429619
AECOM
0.0509845147
AECS Ltd.
0.0109051918
Aerocool Ltd.
0.0109051918
Aeroqual Ltd.
0.0577525103
Affinity Services
0.0249346566
AFT Pharmaceuticals Ltd
0.0587637808
AFTpharmaceuticals
0.0249346566
Agencies for Nutrition Action
0.0217906430
Agile Utilities New Zealand Ltd
0.0169041147
Agknowledge Ltd.
0.0212009962
AgResearch
0.3760716410
Agri-Optic NZ Ltd.
0.0169041147
Agribusiness Group
0.0295790148
AgriGenesis Biosciences Ltd
0.0248896704
AgriHealth NZ Limited
0.0017355927
Agrimm Technologies Ltd
0.0085515239
AgriNova NZ Ltd
0.0089944603
AgriQuality Limited
0.0083317141
Agvance Marketing Ltd.
0.0262813319
Air New Zealand
0.0915449278
Air Quality Ltd.
0.0263746957
Airborne Honey Ltd.
0.0172367328
Akaroa Medical Centre
0.0212473008
Ako Aotearoa National Centre for Tertiary Teaching Excellence
0.0145768290
Akoranga Integrated Health Clinic
0.0117204425
Alan Bell and Associates
0.0125723173
Albany Basin Accident and Medical Centre
0.0073486957
Alcohol Advisory Council of New Zealand
0.0032664850
Alcohol Harm Minimisation Advisory Group
0.0340265148
Alcohol Healthwatch Trust
0.0249346566
Alexandra Lions Club
0.0091827677
Alexandra Medical Centre
0.0212473008
Alfriston College
0.0109051918
All Seasons Pharmacy
0.0249346566
Allan Planning and Research Ltd.
0.0090730520
Allen & Clarke Policy and Regulatory Specialists Limited
0.0555077759
Alphalabs
0.0187458603
Alpine and Polar Processes Consultancy
0.0376639866
Alzheimers Northland
0.0000000000
Amalgamates Solutions and Research Ltd.
0.0191731508
Amity Health Centre
0.0212473008
Ancare New Zealand Ltd.
0.0212473008
Ancare Scientific Ltd
0.0478431997
Anexa FVC
0.0696056383
Anglesea Medical Properties Ltd
0.0548045432
Animal Dermatology NZ
0.0121559609
Animal Health Board New Zealand
0.0279399293
Animals and Marine Surveillance and Investigation Team
0.0169041147
Animation Research Limited
0.0212473008
Antarctic Heritage Trust
0.0109051918
Antarctica New Zelaand
0.0663104085
Antarctica Scientific Limited
0.0168318809
Antipodean Pharmaceuticals
0.0429201429
Aorangi Veterinary Services
0.0024756390
Aotea Pathology Ltd.
0.1298345651
Aotearoa Alcohol and Other Drug Consumer Network
0.0473629359
AP EnerTec Ltd.
0.0000000000
Applied Engineering Research Ltd.
0.0069284140
Applied Research and Technologies Ltd.
0.0096102637
Applied Research Associates New Zealand
0.0091965786
AquaBio Consultants Ltd.
0.0164247640
Aquaculture New Zealand
0.0444266381
Aqualinc Research Ltd.
0.1105440131
Aquanet Consulting Ltd.
0.0169041147
Aquatic Research Solutions Ltd.
0.0325932246
Aranui High School
0.0100397160
ARANZ Geo Ltd
0.0091965786
ARANZ Medical Scanning
0.0163238496
Areograph Ltd.
0.0360664993
ARH Construction
0.0249346566
Aroa Biosurgery
0.1021961716
Arohanui Hospice
0.0055984690
Arotec Diagnostics Ltd.
0.0253678019
Ascot Angiography
0.0295960666
Ascot Women's Cancer Centre of New Zealand
0.0021854512
Asia New Zealand Foundation
0.0504330082
Asphalt Products Limited
0.0148191986
Aspiring Veterinary Service Ltd
0.0184484581
ASR Limited Martine Consulting and Research
0.0325771915
Assa Abloy New Zealand Ltd
0.0212473008
Assistive Technology Ltd.
0.0169041147
Assurity Consulting Ltd
0.0117204425
AsureQuality
0.0336871569
AsureQuality Ltd.
0.0650833395
At the Vets
0.0193797536
Atkinson and Rapley Consulting
0.0169041147
Atlantis HealthCare
0.0249346566
Auckland-Waikato Fish and Game Council
0.0145768290
Auckland Astronomical Society
0.0381483638
Auckland Botanic Gardens
0.0387406275
Auckland Breast Centre
0.0073486957
Auckland City Mission
0.0644644056
Auckland Clinical Studies Ltd.
0.0462106883
Auckland Council
0.2514405100
Auckland Cricket Assn Inc
0.0117204425
Auckland Dermatology
0.0073868398
Auckland District Health Board
0.4334651746
Auckland Eye
0.0456739513
Auckland Heart Group
0.0543955521
Auckland Institute of Studies
0.0151004270
Auckland International Airport Limited
0.0117204425
Auckland Museum
0.1651970874
Auckland Refugee Community Coalition
0.0249346566
Auckland Regional Council
0.0249346566
Auckland Southern Cross Hospital Group
0.0322833524
Auckland Transport
0.0249346566
Auckland Zoo
0.1238622030
Aurecon
0.0621103982
Australian and New Zealand College of Anaesthetists
0.0357429619
AUT University
0.4700462773
Automation Design Ltd
0.0025280601
Aviation Industry Association of New Zealand Inc
0.0000000000
Avivet Ltd
0.0262813319
Avocado Industry Council
0.0083317141
Babbage Consulting Ltd.
0.0556394773
Ballance Agri-Nutrients Limited
0.0841401665
Bank of Scotland
0.0249346566
Bartonk Solutions
0.0108361949
Batten Animal Research Network
0.0297988246
Baxter Healthcare Limited
0.0778439353
Bay Audiology
0.0148191986
Bay of Plenty District Health Board
0.2006176989
Bay of Plenty Polytechnic
0.1214434910
Bay of Plenty Regional Council
0.0498932908
Bay Urology
0.0188880385
Bayer CropScience New Zealand
0.0096082207
Bayleys Property Services
0.0249346566
BC Consulting Ltd.
0.0105686304
BCRL Energy Limited
0.0015532672
Beca
0.1085507044
Beef and Lamb New Zealand
0.0653301154
Bennett Scientific
0.0600119714
Benthic Science Ltd.
0.0303203528
Berryworld Ltd
0.0171016191
Best Practice Advocacy Centre
0.0461819574
Beta Solutions
0.0418387713
Bethesda Care
0.0322833524
Betta Bees Research Ltd
0.0212473008
Better Border Biosecurity
0.0175144817
BHU Future Farming Centre
0.0233707224
Bickler Consultants Ltd.
0.0570871492
BikeNZ
0.0148191986
Bio Soil and Crop Ltd
0.0000000000
Bioactives Research New Zealand
0.0647089028
Biodiscovery New Zealand Ltd.
0.0625963784
Biomarine Ltd.
0.0249346566
Biomatters Ltd.
0.0461819574
Biometrics Matters Ltd
0.0561137714
Biopolymer Network Ltd
0.0662200775
Biosecurity New Zealand
0.0334589485
BioSylve Forest Science NZ Ltd.
0.0069284140
BirdLife Global Seabird Programme
0.0088708385
Blind Foundation
0.0169041147
BLIS Technologies Ltd.
0.0453709988
Blue Water Marine Research
0.0340077087
Blues Rugby Club
0.0000000000
Bodeker Scientific
0.0599799055
Body Aid Clinic Ltd
0.0212473008
Boffa Miskell Ltd
0.1279181462
Bomac Laboratories Ltd
0.0516696117
Boulcott Hospital
0.0050021543
Braemar Hospital
0.0344357356
BRANZ Ltd.
0.1304195764
Bream Bay Medical Centre
0.0249346566
Breast Care and Screening Services
0.0323214964
Breast Surgeons' Society of New Zealand
0.0249346566
Breen Consulting
0.0181546078
Brian Ricketts Geological Consulting Limited
0.0077405813
Broadway Medical Centre
0.0330143899
Broadway Surgical Clinic
0.0136782023
Broken Hills Gold Co
0.0249346566
Brownrigg Agriculture
0.0068977582
Bruce Shallard and Associates
0.0000000000
Bunnythorpe School
0.0091827677
Cadwallader Tree Consultancy
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Cahill Animal Hospital
0.0169041147
CAL Engineering Management
0.0153758990
Callaghan Innovation
0.2234003482
Cambridge Clinic
0.0339592927
Cambridge Veterinary Services
0.0121559609
Cameron Medical Clinic
0.0472233491
Campbell and Associates Ltd.
0.0083317141
Cancer Control Council of New Zealand
0.0478920383
Cancer Society of New Zealand
0.0860232744
Canterbury Charity Hospital Trust
0.0372006247
Canterbury Civil Defence and Emergency Management Group
0.0119788176
Canterbury District Health Board
0.4357203327
Canterbury Earthquake Recovery Authority
0.0442329677
Canterbury Health Ltd
0.0792525326
Canterbury Medical Imaging
0.0278119441
Canterbury Museum
0.1900636996
Canterbury Rugby Football Union and Crusaders
0.0129927456
CanZealand Geoscience Ltd
0.0082679590
Cape Kidnappers and Ocean Beach Wildlife Preserve
0.0255722930
Cape Sanctuary
0.0376177111
Capital and Coast District Health Board
0.3177595138
Capital Eye Specialists
0.0121523837
Capital Research
0.0291705251
Carbon Partnership
0.0091827677
Cardiac Inherited Disease Group
0.0357429619
Care of Orca Research Trust
0.0004217605
Carey Baptist College
0.0249346566
Carroll Consulting ltd
0.0224745256
Carson Associates Ltd.
0.0069284140
Carter Holt Harvey Ltd.
0.0545001079
Carter National Observatory
0.0326965585
Cashmere Health
0.0217906430
Catch Ltd.
0.0249346566
Catmed
0.0071244369
Cawthron Institute
0.2826406171
CBG Health Research Limited
0.0741632077
Centennial Health
0.0223625034
Center for Backyard Astrophysics
0.0046759434
Central and Southern New Zealand Craniofacial Program
0.0430994673
Central City Vets
0.0173363916
Central Otago Tourism
0.0212473008
Central Stories Museum
0.0091827677
CentralMed
0.0774218017
Centre for Backyard Astrophysics
0.0948879961
Centre for Clinical Research and Effective Practice
0.0742382356
Centre for Dairy Excellence
0.0173363916
Centre for Minerals Environmental Research (CMER)
0.0228005680
Centre for Research Evaluation and Social Assessment
0.0033351276
Centre for Youth Health in South Auckland
0.0330143899
CH and Associates
0.0310106277
ChangeMakers Refugee Forum
0.0000000000
Chatham Rock Phosphate Ltd.
0.0000000000
Chemipreneur Ltd.
0.0384093576
Chemistry Communications
0.0322833524
Chiefs Super Rugby Franchise
0.0222977389
Child and Youth Health
0.0371987277
Child Poverty Action Group
0.0249346566
Chilton Saint James School
0.0000000000
Chiptech Ltd
0.0217906430
Christchurch City Council
0.1258794787
Christchurch Emergency Care Foundation
0.0739506089
Christchurch Polytechnic Institute of Technology
0.1781144112
Christchurch Psychologists' Office
0.0360664993
Christchurch Vascular Group
0.0497172699
City Care Ltd
0.0148191986
City Fitness
0.0460746398
Civil Aviation Authority
0.0418387713
Claro
0.0249346566
ClearSight Consultants Ltd
0.0572131979
Clement and Associates Ltd
0.0154066930
Clendon Burns and Park Consulting Engineers
0.0111340106
CLIMsystems Ltd.
0.0109051918
Clinical Horizons
0.0311176247
Clinical Systems
0.0080797332
Clutha Veterinary Association
0.0237229397
Coast and Catchment Ltd
0.0465901427
Coast to Coast Health Centre
0.0073486957
Coastal and Aquatic Systems Ltd
0.0537592324
Coastal Systems (NZ) Ltd.
0.0031067036
Coastline Consultants
0.0069284140
Cognition Education Limited
0.0249346566
Cognosco
0.0395351994
Colgate-Palmolive Ltd
0.0148191986
Colin Christian Ltd.
0.0212473008
Collins Carriers Ltd.
0.0085515239
Colmar Brunton
0.0249346566
Columba College
0.0212473008
Common Ground Ltd
0.0356766685
Commtest Instruments Ltd
0.0148191986
Community Clinic for Sexual Health and Contraception
0.0249346566
Compac Sorting Equipment Ltd.
0.0332663707
Compac Technologies
0.0169041147
Compass Health
0.0358004066
Compusoft Engineering Limited
0.0249346566
Compusoft Engineering Ltd.
0.0255722930
Comtel System Ltd.
0.0180783636
Comvita New Zealand Ltd.
0.0576211479
Connectos Consulting
0.0385790078
Connovation Ltd.
0.0804404351
Conservation and Environmental Management
0.0164100305
Construction Techniques Ltd.
0.0397538552
Consulting Dietitians Ltd.
0.0357429619
Contact Energy Ltd.
0.0372421227
Contract Landscapes Ltd
0.0031067036
CORE Education Ltd.
0.0358398484
Cosgrove
0.0148191986
Counties Manukau District Health Board
0.3240362737
Covec Ltd
0.0547334813
CPG New Zealand Ltd.
0.0169041147
Crawford Medical Centre
0.0255722930
CRL Energy Ltd.
0.0622935069
Cromwell College
0.0145768290
Cropmark Seeds Limited
0.0275757006
Crown Fibre Holdings Limited
0.0000000000
CURT St George's Medical Centre
0.0717204409
Cuttriss Consultants Ltd
0.0082679590
Cymbiotix Group Limited
0.0366550992
Cyperus Ltd
0.0610011560
Dairy Consultants Ltd.
0.0032528812
Dairy Goat Co-operative (NZ) Ltd.
0.0608505861
Dairy Production Systems Ltd.
0.0002339632
DairyNZ
0.1976925650
David Butler Associates Ltd
0.0169041147
Davidson Environmental Ltd.
0.0608123459
DaVinci Clinic
0.0009407940
DCM Process Control Ltd.
0.0249346566
DEA Research Software Surgery Ltd.
0.0249346566
Deepwater Group Ltd
0.0154066930
DeerNZ
0.0083317141
Deloitte
0.0779052706
Department of Conservation
0.3434545723
Department of Corrections
0.0148191986
Development Action
0.0145768290
Development By Design
0.0145768290
Devon Medical Centre
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DHI Water and Environment
0.0031407143
Diabetes Otago Inc
0.0212473008
Diagnostic Laboratory
0.0438226952
Diagnostic Medlab
0.1020326684
Digestive Health Services
0.0321118376
Digital Sensing Limited
0.0395114857
Disability Connect
0.0255722930
Disability Resource Centre
0.0385790078
Diversity NZ
0.0385790078
DM Consultants
0.0534911546
DNA Investments Ltd.
0.0067545733
Dnature diagnostics and research Ltd.
0.0643217854
Doctors for Sexual Abuse Care
0.0256275039
Donaghys Industries
0.0085447751
Donald Beasley Institute
0.0675474430
Dorothy-Jean and Associates
0.0093686431
Dovedale Ltd.
0.0630860720
Downer EDI Works Limited
0.0145215529
Dr. Malcolm McKellar Ltd.
0.0028159529
Dragonfly Ltd.
0.0643386817
Drummond Food Science Advisory Ltd.
0.0212473008
Dumpark Data Science
0.0003351217
Duncan Cotterill
0.0227419482
Dunedin City Council
0.0250801257
Dunedin Heat Pumps Limited
0.0212473008
Dunedin South Veterinary Clinic
0.0169041147
Dunning Thornton Consultants Ltd.
0.0280413602
Dynamic Controls Ltd.
0.0301367406
Dynatest
0.0292907106
Dyspraxia Support Group of New Zealand
0.0321118376
Earthquake Commission
0.0608212113
Earthtech Consulting Limited
0.0255722930
Eastern Institute of Technology
0.1355536810
Eastern Region Fish and Game
0.0212223159
Eastern Suburbs Association Football Club (ESAFC)
0.0418387713
Eastland Veterinary Services Ltd.
0.0193797536
Eaton Power Quality Ltd.
0.0148191986
ECG Consultants
0.0169041147
Eco-Vista Photography and Research Ltd.
0.0834663789
Eco Nomos Ltd.
0.0184502693
Eco Research Associates Ltd
0.0783329188
ECoast Limited
0.0134399958
EcoGecko Consultants Ltd.
0.0535708193
Ecosynergy Group Ltd (EGL)
0.0145768290
Ectus Ltd
0.0109051918
Edmund Lawler and Associates Limited
0.0145768290
Education House
0.0000000000
Education Review Office
0.0249346566
Educational Leadership Project
0.0109051918
Electricity Authority
0.0543306842
Eli Lilly and Company (New Zealand) Limited
0.0322162022
Elmwood Orthopaedics
0.0222124035
Eltham District Veterinary Services
0.0351889468
Endoscopy Auckland
0.0281588178
Energy Efficiency and Conservation Authority
0.0570927062
Energy Solution Providers Ltd.
0.0085515239
EnForm Tech
0.0154523504
Enigma Publishing Ltd.
0.0357633071
Ensys Ltd
0.0148191986
Entecol Ltd.
0.0655898892
Enviro-Mark Solutions Ltd.
0.0148191986
Enviro Research
0.0096170142
Environment Canterbury
0.1589865237
Environment Protection Authority(EPA)
0.0392141743
Environmental Management Services
0.0082679590
Environmental Restoration Ltd
0.0069284140
ENZO Nutraceuticals Limited
0.0337630125
Epi-interactive
0.0598731008
Epsom Girls Grammar School
0.0249346566
Equine Health Association
0.0067545733
ERA Ecology
0.0621586728
Erin Park
0.0424816145
ESR
0.3757277751
Etec Crop Solutions
0.0083317141
Eudyptes EcoConsulting Ltd
0.0298112226
Explore NZ
0.0169041147
Eye Institute
0.0357429619
Far North District Council
0.0197207777
Farm Cove Observatory
0.0926398885
Feilding Medical Centre
0.0379873515
FEM Ltd.
0.0000000000
Fern Research Foundation
0.0202866077
Ferndale School
0.0148191986
Fertility Associates
0.0819656056
Financial Markets Authority
0.0145768290
Fish and Game NZ
0.0310106277
Fisher and Paykel Appliances
0.0249346566
Fisher and Paykel Healthcare Ltd.
0.1224453025
Fishing Vessel Management Services Ltd.
0.0203179504
FitzRoy of Merivale
0.0240019662
Fletcher Construction Co
0.0270640959
FMR GROUP LTD
0.0101758024
Fonterra
0.2380157231
Food and Bio-based Products Group
0.0346130460
Food and Health Group
0.0346130460
Foot Science International Ltd.
0.0212473008
Forensic and Industrial Science Ltd
0.0249346566
Forest and Bird
0.0512985933
Forever Beech Ltd.
0.0148191986
Foundation for Arable Research
0.0369526604
Foundation for Research Science and Technology
0.0169041147
Fox and Associates-Consulting Surveyors
0.0230871576
Fred Hollows Foundation
0.0536255208
Fresenius Medical Care Australia Pty Ltd (New Zealand Branch)
0.0330143899
Freshport NZ Ltd
0.0085515239
Frontier Global Ltd.
0.0249346566
Fruitfed Supplies
0.0094809400
Fruition Horticulture
0.0265793209
FullSpectrum Ltd.
0.0109051918
Fulton Hogan Ltd.
0.0501049765
Future Forests Research
0.0069284140
Future Steps
0.0610011560
FuturebyDesign Ltd.
0.0439934000
FutureMATH Ltd.
0.0015017680
Gallagher Animal Management Systems
0.0109051918
Gambling Helpline
0.0286245572
Genesis Research & Development Corporation Ltd
0.0461819574
Genetic Technologies Ltd.
0.0169041147
Gentrack Limited
0.0160004160
Geoenvironmetal Services
0.0025725030
GEOKEM
0.0262567192
Geomarine Research
0.1307263209
Geoscience Consulting Ltd
0.0249346566
Geotech Consulting Ltd
0.0239085786
Geothermal Engineering Ltd
0.0249346566
Geoventures Limited
0.0212473008
GF McLaren Research Limited
0.0085447751
GHD Centre Level Napier St.
0.0249346566
GHD Limited
0.0000000000
Gillies McIndoe Research Institute
0.0911656099
Gisborne District Council
0.0111340106
Glass Earth Gold Ltd
0.0212473008
Glenview Medical Centre
0.0332561553
Global Action for Health Equity Network (HealthGAEN)
0.0169041147
Global Public Health Company Ltd
0.0673236461
GNS Science
0.3315850368
Golden Bay Cement
0.0255722930
Golder Associates (NZ) Ltd
0.1044139017
Good Life Research Centre Trust
0.0151073910
Google
0.0145768290
Greater Wellington Regional Council
0.0728700020
Green Lane Hospital
0.0073486957
Greenweaver Architecture Ltd
0.0178287964
Greerton Early Childhood Centre
0.0257243904
Gribbles Veterinary
0.0992850638
GroPlus Ltd.
0.0000000000
Ground Investigation Ltd
0.0249346566
Growth Solutionz
0.0000000000
Guardian Health Care (Bupa)
0.0424816145
Hagley Community College
0.0148191986
Hally Labels
0.0145768290
Hamilton Eye Clinic
0.0249346566
Hamilton Sacred Heart College for Girls
0.0109051918
Hamilton Veterinary Services
0.0169041147
Hamilton Zoo
0.0927657568
Hanham Consultants
0.0249346566
Hanmer Clinic Tauranga
0.0212473008
Hapai Te Hauora Tapui Ltd
0.0366550992
Harker Underground Construction Limited
0.0151981595
Harris Consulting
0.0209783294
Hauora Heretaunga
0.0249346566
Hauora Waikato Group
0.0492256111
Hauraki Maori Trust Board
0.0411532437
Hawke's Bay Alcohol and Drug Service
0.0416621294
Hawke's Bay District Health Board
0.2058971165
Hawke's Bay Regional Council
0.0911863123
Hawkins Watts
0.0249346566
Health Alliance
0.0309912817
Health Care Aotearoa
0.0148191986
Health New Zealand Ltd.
0.1496627014
Health Outcomes Associates Ltd.
0.0249346566
Health Partners Consulting Group
0.0874820562
Health Promotion Agency
0.1078352175
Health Quality and Safety Commission
0.0785713611
Healthscope Laboratories
0.0041860189
HealthWEST
0.0571097128
Heart Foundation of New Zealand
0.0470104811
Heavy Engineering Research Association
0.0616612301
HEB Construction
0.0015883053
Heinz Wattie's
0.0257653650
Heke Consulting
0.0249346566
Helios Integrative Medical Centre
0.0000000000
Hemptech
0.0109051918
Henderson Medical Centre
0.0595109013
Henderson Valley Primary School
0.0109051918
Hepatitis Foundation of New Zealand
0.0961128542
Herbert Morton Accountants
0.0109051918
Heretaunga Health
0.0357429619
Heritage New Zealand Pouhere Taonga
0.0249346566
High Performance Sport New Zealand
0.0421276382
Highnam Associates Ltd.
0.0249346566
Hill Laboratories Ltd.
0.0754071544
Hiway Geotechnical
0.0249346566
HodderBalog Social and Scientific Research
0.0145768290
Holcim (NZ)
0.0000000000
Holmes Consulting Group
0.0765103830
Holmes Fire and Safety
0.0408654475
Horizons Regional Council
0.1036948576
Horowhenua Community Practice
0.0212473008
Horowhenua Library Trust
0.0000000000
Horteye Ltd
0.0087581371
HortPlus
0.0117560195
Hospice New Zealand
0.0728864487
Hospice Palliative Care Education
0.0484356873
Hospice Waikato
0.0374843300
Hot Solutions Ltd.
0.0341312352
Humes Pipeline Systems
0.0249346566
Huntly Community Link
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Hurricanes Rugby
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Hush Interiors Ltd
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Hutt Valley District Health Board
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Hyland Consultants
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Hyland Fatigue Earthquake Engineering
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Hyperbaric Health
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IAG
0.0148191986
Ian Kusabs and Associates Limited
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Ian McLean Consultancy Services Ltd.
0.0249346566
Ichthyo-niche
0.0446304212
IGENZ Ltd
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ILR
0.0496341794
Immunisation Advisory Centre
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Inclusive Education Action Group
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Independent Petroleum Laboratory
0.0332663707
Indufor Asia-Pacific Ltd
0.0116772984
Infoics Limited
0.0106608986
Inform Planning Ltd
0.0367563556
Infrastructure Decisions Limited
0.0399912723
Inglewood Veterinary Services
0.0218335109
Injury Prevention Aotearoa
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Inland Revenue
0.0316922747
Innate Immunotherapeutics Limited
0.0694477081
Innate therapeutics
0.0194160608
Inner City Women's Group
0.0249346566
Inner Zest Ltd.
0.0249346566
INR Online Ltd
0.0058923147
Insect Science Solutions
0.0186163317
Insights MSD
0.0023543578
Inspiring Ltd.
0.0481689618
Institution of Professional Engineers New Zealand
0.0265509510
Intellectual Property Office of New Zealand
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Intensive Care Flight Paramedic
0.0189598211
Interactionz
0.0109051918
InterAg
0.0739432749
International Animal Welfare Consultants Limited
0.0169041147
International Earth Sciences IESE Ltd.
0.0477794447
International Pacific College
0.0169041147
International Student Ministries of New Zealand
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International Telematics Ltd.
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Interpine
0.0100114347
Interpine Forestry Ltd
0.0127740846
Intus Digestive and Colorectal Care
0.0212473008
Invenco Group Ltd.
0.0249346566
Investigation Geology Ltd
0.0151981595
IPENZ
0.0384282773
Irrigation New Zealand Inc.
0.0108985458
Isolytix
0.0212473008
IZON Science Ltd.
0.0905170390
Jackett Consulting
0.0025884288
Jacobs Engineering
0.0270640959
Jade Software Corporation
0.0360664993
James and Monroe
0.0286245572
JMR Distributors Ltd
0.0169041147
John Jones Steel
0.0407710853
John Wood Consulting
0.0409728157
Johne's Management Limited
0.0354640995
Jowett Consulting Ltd.
0.0260880823
JRA (NZ) Ltd.
0.0249346566
Julian King and Associates Limited
0.0181570010
Ka Mau Te Wero
0.0091827677
Kaikorai Valley College
0.0212473008
Kaikoura Ocean Research Institute Inc.
0.0334985785
Kaipaki Veterinary Services
0.0169041147
Kaipara District Council
0.0197207777
Kapiti Coast District Council
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Karori Sanctuary Trust
0.0359299169
Katoa Ltd
0.0626235739
Kea Conservation Trust
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KEA Consultant
0.0000000000
Keratec Ltd.
0.0306245180
Kidney Health New Zealand
0.0828530096
Kina Families and Addictions Trust
0.0432853893
Kinetic Engineering Design
0.0249346566
Kingdom Clinic
0.0258575467
Kiwi Well Evaluation Ltd
0.0358241298
Kiwi Wildlife
0.0057097786
Kiwicap Research Ltd
0.0000000000
Kiwikiwi Research and Evaluation Services
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Kono Horticulture Limited
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Koru Environmental Consultants Ltd
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Koti Technologies
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Kumeu Observatory
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Kurahaupo Consulting
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KVB Kunlun New Zealand Limited
0.0169041147
Labtests
0.0876471356
Lake Hawea Institute of Cryodynamics
0.0293960276
Lakes District Health Board
0.1033215235
Land Information New Zealand
0.0560549009
Landcare Research
0.3682732746
Landcorp Farming Limited
0.0514818144
Langimalie Clinic
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LanzaTech NZ Ltd.
0.0281757147
Lassey Research and Education Ltd
0.0090730520
Lateral Technology
0.0249346566
Laura Fergusson Trust
0.0321118376
Law Commission
0.0145768290
LeaderBrand Produce Ltd.
0.0085681181
Learning for Sustainability
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Leather & Shoe Research Association of New Zealand
0.0310042642
Leinster Orthopaedic Centre
0.0031013897
Levare Limited
0.0357429619
Levin and Horowhenua Veterinary Centre
0.0176209316
Lewis and Barrow Ltd.
0.0153758990
LIC
0.0958357277
Life Technologies Ltd.
0.0148191986
LightBox Psychology Services
0.0360664993
Lincoln Agritech Ltd.
0.1013874056
Lincoln University
0.3429573541
Lincolne Scott Ltd.
0.0148191986
Lindis Consulting
0.0175531269
Linnaeus Laboratory
0.0125693892
Litmus
0.0603669014
Livestock Solutions and Services
0.0169041147
Living Cell Technologies NZ Ltd.
0.0330143899
Local Government New Zealand
0.0305557298
Logjiztix Ltd
0.0025785973
Lowe NZ
0.0090730520
Lucas Industries (NZ) Ltd.
0.0249346566
LWT Animal Nutrition Ltd.
0.0173363916
MacMurray Hypertension Clinic Ltd
0.0322833524
MAGAK
0.0077405813
Magic Sparks Early Learning and Development Centre
0.0438025446
Magritek Limited
0.0395114857
Makoura College
0.0145768290
Malaghan Institute of Medical Research
0.1250673199
Male Survivors of Sexual Abuse Trust
0.0148191986
Manaaki Te Awanui
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Manaia Health Primary Health Organisation
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Manawatu Diagnostics
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Mangere Community Health Trust (Primary Health Organisation)
0.0556229171
Manukau Institute of Technology
0.1442610388
Manukau SuperClinic
0.0249346566
Manurewa South School
0.0249346566
Maori Hill Clinic
0.0212473008
Maori Pharmacists Association
0.0636178473
Maramatanga Consultants Ltd
0.0169041147
Marine Fisheries Research Services Limited
0.0065355474
Marine Wildlife Research Ltd
0.0392083571
Marinoto Clinic
0.0346989044
Mark L Batchelar Consulting Engineers
0.0148191986
Market Economics Ltd.
0.0169041147
Marlborough Wine Research Center
0.0739568360
MARS Bioimaging Ltd
0.0587749017
Marshall Day Acoustics Ltd.
0.0402873112
Mary Potter Hospice
0.0411025740
Massey University
0.6779365323
Masters Consulting Ltd.
0.0065355474
Matakina Technology Ltd
0.0388296394
Matamata Medical Centre
0.0332134020
Matamata Veterinary Services Ltd
0.0277859271
MBCentury Ltd
0.0249346566
McConnell Dowell Constructors Ltd.
0.0023284728
McLaren Research Ltd.
0.0083317141
McManus Geotech Ltd.
0.0128106393
Medical Council of New Zealand (MCNZ)
0.0025245226
Medical Research Institute of New Zealand
0.2167954277
Medlab Central
0.0900108481
Melanoma Unit
0.0348275019
Member International Neuropsychological Society
0.0212473008
Mental Health Education Resource Centre
0.0148191986
Mental Health Foundation of New Zealand
0.0526470766
MercyAscot Hospitals
0.1293044152
Meridian Energy Ltd.
0.0283020037
Mesynthes Ltd.
0.0566984213
Meteorological Service of New Zealand Ltd.
0.1119667030
Methanex
0.0185204091
MetOcean Solutions Ltd.
0.0442112677
Microfossil Research Ltd
0.1031697792
MidCentral District Health Board
0.2245256123
Midland MRI
0.0109051918
Midland Regional Forensic Services
0.0249346566
Midlands Health Network
0.0357697137
Midwifery Council of New Zealand
0.0336253322
Mighty River Power Ltd.
0.0792937180
Millar Instruments
0.0422785094
Milton Health Centre
0.0223625034
Ministry for Primary Industries
0.2708909700
Ministry for Primary Industry
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Ministry for the Environment
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Ministry of Business Innovation and Employment
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Ministry of Civil Defence and Emergency Management
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Ministry of Education
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Ministry of Foreign Affairs and Trade
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Ministry of Health
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Ministry of Justice
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Ministry of Pacific Island Affairs
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Ministry of Social Development
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Ministry of Transport
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Mission Heights Primary School
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MLB Consulting Engineers
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Molehill Astronomical Observatory
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Moorhouse Medical Clinic
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Morrison Consultants Ltd
0.0052882317
Motu Economic and Public Policy Research
0.1421051798
Mountains to Sea Conservation Trust
0.0465901427
MSD Animal Health Ltd
0.0250387059
Mt. Albert Psychological Services Ltd
0.0036890855
Mulgor Consulting Ltd.
0.0176761327
Muscular Dystrophy Association of New Zealand
0.0856400059
MWH New Zealand Ltd
0.0397538552
N-Squared Software
0.0395114857
NaeNae Medical Centre
0.0150626900
National Addiction Centre
0.0212473008
National Association of Steel-Framed Housing Inc
0.0264721582
National Council of Women of New Zealand
0.0231509127
National Heart Foundation of New Zealand
0.1102448403
National Library of New Zealand Te Puna Matauranga O Aotearoa
0.0227350585
National Maori Health Workforce Organisation
0.0212473008
Natural Resource Assessors
0.0455295377
Needle Exchange Programme NZ
0.0473629359
Nelson Forests Limited
0.0217476125
Nelson Marlborough District Health Board
0.1696096864
Nelson Marlborough Fish and Game
0.0282948475
Nelson Marlborough Institute of Technology
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Nelson Marlborough Regional Council
0.0356766685
Neonatal Intensive Care Unit
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NetSafe
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NetValue
0.0000000000
Neuren Pharmaceuticals
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Neurological Foundation of New Zealand
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New Brighton Health Care
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New Image Group Ltd
0.0249346566
New River Ltd
0.0217906430
New Zealand Academy of Sport
0.1020567927
New Zealand Aerial Mapping
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New Zealand Agricultural Greenhouse Gas Research Centre
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New Zealand Agriseeds Limited
0.0252358287
New Zealand AIDS Foundation
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New Zealand Aluminium Smelters Limited
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New Zealand Antarctic Institute
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New Zealand Arable
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New Zealand Association of Optometrists
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New Zealand Avocado Growers Association
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New Zealand BioSecure Entomology Laboratory Research
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New Zealand Blood Service
0.1129332944
New Zealand Brain Research Institute
0.1117414112
New Zealand Breast Cancer Foundation
0.0321118376
New Zealand Centre for Conservation Medicine (NZCCM)
0.1207957209
New Zealand Climate & Health Council
0.0461819574
New Zealand College of Chiropractic
0.0366550992
New Zealand College of Midwives
0.1309642552
New Zealand Cot Death Association
0.0255722930
New Zealand Council for Educational Research (NZCER)
0.0572053341
New Zealand Defence Force
0.1272999106
New Zealand Dental Association
0.0227419482
New Zealand Employment Service and Work and Income New Zealand
0.0003697415
New Zealand Familial Gastrointestinal Cancer Service
0.0615584624
New Zealand Forestry Ltd
0.0072469314
New Zealand Geotechnical Society Ine (NZGS)
0.0000000000
New Zealand Guidelines Group
0.0556901454
New Zealand Gynaecological Cancer Foundation
0.0342807340
New Zealand Heart and Lung Transplant Service
0.0438226952
New Zealand Heavy Engineering Research Association
0.0445802104
New Zealand Homebased Early Childhood Education Association
0.0243757323
New Zealand Institute for Plastic and Cosmetic Surgery
0.0212473008
New Zealand Institute of Community Health Care
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New Zealand Institute of Economic Research
0.0973370743
New Zealand Institute of Medical Laboratory Science
0.0336369978
New Zealand Institute of Rural Health
0.0461819574
New Zealand Kiwi Foundation
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New Zealand Medical Association
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New Zealand Medical Students' Association
0.0461819574
New Zealand National Eye Bank
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New Zealand National LCP Office
0.0394397671
New Zealand Needle Exchange Programme
0.0796199837
New Zealand Nurses Organisation
0.0684361320
New Zealand Olympic Committee
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New Zealand Organisation for Rare Disorders (NZORD)
0.0212473008
New Zealand Parliament
0.0145768290
New Zealand Police
0.0798415549
New Zealand Qualifications Authority
0.0145768290
New Zealand Refining Co. Ltd.
0.0148191986
New Zealand Rheumatology Association
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New Zealand Rugby Union
0.0587263709
New Zealand School Acupuncture and Traditional Chinese Medicine
0.0148191986
New Zealand School of Music
0.0145768290
New Zealand Seafood Industry Council Ltd
0.0207596165
New Zealand Society for Earthquake Engineering (NZSEE)
0.0000000000
New Zealand Spinal Trust
0.0321118376
New Zealand Tertiary College
0.0366550992
New Zealand Timberlands Ltd
0.0012189605
New Zealand Transport Agency
0.0488861956
New Zealand Treasury
0.0944211056
New Zealand Underwater Heritage Group
0.0111840626
New Zealand Veterinary Pathology Ltd.
0.0287478185
New Zealand Winegrowers
0.0340077087
Newman Energy Research
0.0148191986
Newtown Medical Centre
0.0461819574
NextWindow Ltd
0.0461819574
Ngati Porou Hauora
0.0255722930
Ngati Whakaue Tribal Lands Inc
0.0069284140
Nielsen Company
0.0273908222
NIU Development Incorporated
0.0535592138
NIWA
0.3638731488
Norske Skog Tasman
0.0249346566
North Canterbury Veterinary Clinics
0.0195312769
North Shore Hospice
0.0474634045
North Shore International Academy
0.0278093065
Northcott Research Consultants Ltd.
0.0787596026
Northern Cancer Network
0.0357429619
Northern Region IDEA Services
0.0249346566
Northern Regional Alliance
0.0138842432
Northern Southland Veterinary Services
0.0030384063
Northland District Health Board
0.1590355529
Northland Regional Council
0.0735202199
NorthTec
0.0704160052
Novare Design Ltd.
0.0148191986
Numcore Ltd.
0.0249346566
Numinos Ltd.
0.0249346566
Nurse Maude Association
0.0603437647
Nutrigenomics New Zealand
0.0807950034
Nutrition Society of New Zealand
0.0212473008
NZ Oil and Gas
0.0228447881
NZ Parsa Tiling Limited
0.0148191986
NZFOCUS (NZ) Ltd.
0.0249346566
NZX Limited
0.0249346566
O'Kane Consultants (NZ) Ltd
0.0440321805
Oamaru Hospital
0.0212473008
Odyssey House
0.0249346566
Office of the Health and Disability Commissioner
0.0249346566
Office of the Parliamentary Commissioner for the Environment
0.0395031204
Omahu Urology Clinic
0.0291705251
OMV New Zealand Ltd.
0.0556182741
Oncology Surgery Ltd.
0.0445655922
Open Polytechnic of New Zealand
0.1254651930
OPRA Consulting Group
0.0148284179
Optimal Clinical Trials
0.0453398280
Opus International Consultants Ltd
0.1038084801
Oracle New Zealand
0.0145768290
Oral Health Centre
0.0320556060
Orange Consulting
0.0212473008
Orb Solutions
0.0467293216
Organ Donation New Zealand
0.0474634045
Oritain Global Ltd.
0.0212473008
Ornithological Society of New Zealand
0.0473341831
Orokonui Ecosanctuary
0.0358241298
OSPRI
0.0799331079
Otago Community Hospice
0.0398993243
Otago Computational Modelling Group Ltd.
0.0548535325
Otago Daily Times Collective
0.0212473008
Otago Girls High School
0.0776629011
Otago Museum
0.0866294657
Otago Polytechnic
0.1537147673
Otago Regional Council
0.0562895940
Otahuhu College
0.0571097128
Otakaro Pathways Ltd
0.0191962510
Otorohanga Dental Surgery
0.0212473008
OTRS Group Ltd
0.0516319471
Outome Management Services
0.0249346566
P.N. Plimmer and Associ.
0.0255722930
PA Handford and Assoc. Ltd.
0.0094564741
Pacific Brands
0.0249346566
Pacific Edge Biotechnology Ltd.
0.0886180172
Pacific Health Research and Development Foundation
0.0418387713
Pacific Radiology Group
0.1243806845
Pacific Women's Health Research and Development Unit
0.0498793202
Pakuranga Medical Centre
0.0082863505
Palaecol Research Ltd
0.0933223016
Palmerston North City Council
0.0173363916
Palmerston North City Library
0.0145768290
Pansophy Ltd
0.0356766685
Papamoa Pines Medical Centre
0.0864889945
Paraparaumu College
0.0602954152
Paric Limited
0.0249346566
Parkinson's New Zealand
0.0249346566
Parresia Research Limited
0.0249346566
Parsons Brinckerhoff
0.0249346566
Pasifika Horizon Healthcare
0.0249346566
Pasifika Medical Association
0.0306534491
Pasifika Research Ltd
0.0161383263
Pathlab
0.0377303774
Patients First
0.0243650995
Paton-Simpson Associates Limited
0.0329677433
Pattle Delamore Partners Ltd
0.0161869526
Pegasus Health Ltd
0.0767877909
Penny and Associates Ltd
0.0511284497
Perinatal and Maternal Mortality Review Committee
0.0704337275
Petersgate Counselling Centre
0.0148191986
PF Olsen and Company Ltd
0.0103299521
PGG Wrightson Seeds Ltd.
0.0360872003
PHARMAC
0.0739195634
Pharmaceuticol Ltd
0.0271904282
Pharmacy Guild of New Zealand
0.0249346566
PharmTech Service Limited
0.0486575964
Philosophy of Education Society of Australasia
0.0249346566
Photonz Corporation Ltd
0.0249346566
Pictor Ltd.
0.0249346566
Pingar Research
0.0111840626
Pinnacle Group Ltd
0.0288352122
PipeTechnologies
0.0270640959
Pipfruit New Zealand
0.0352757922
Planning Consultants Ltd
0.0367563556
Plant and Food Research
0.3341419215
Plant Protection Chemistry NZ Ltd
0.0157330438
PlusGroup Limited
0.0269208233
Pohatu Penguins
0.0288339329
Polybatics Ltd.
0.0314809437
Porirua City Council
0.0212473008
Ports of Auckland Limited
0.0255722930
Positive Thinking Ltd
0.0249346566
Possum Observatory
0.0970279870
Potter Building Services Ltd.
0.0501704854
Power Co Ltd.
0.0249346566
Power Systems Consultants New Zealand Ltd
0.0016479868
PowerbyProxi Ltd.
0.0249346566
Powerhouse Ventures Ltd
0.0256837355
Practitioners First Limited
0.0267575828
Presbyterian Church of New Zealand
0.0357429619
PriceWaterhouse Coopers (PwC)
0.0664643664
Priestley Structural Engineering
0.0424605298
Private Endodontic Practice
0.0212473008
ProCare Health Limited
0.0583832284
Prohealth Physiotherapy Ltd
0.0230702269
Promisia Ltd
0.0234461033
Proteus Wildlife Research Consultants
0.0459224042
Psychological Service
0.0249346566
Psychology Centre
0.0323214964
Pultron Composites Ltd.
0.0178336058
Pyrotek
0.0213941598
Q-Bit Ltd.
0.0233707224
QE Health
0.0357429619
Qnique Ltd
0.0607587864
QStar Solutions Ltd.
0.0180711659
Quadradix
0.0249346566
Quay Park Medical Centre
0.0569902627
Queens Academic Group
0.0249346566
Quest Integrity Group Ltd.
0.0648212014
Quigley and Watts Ltd.
0.0321118376
Quin Environmentals(NZ) Ltd.
0.0338213194
Quintessence Developments Ltd.
0.0172367328
Quit Group
0.0819954942
Radiata Pine Breeding Company
0.0069284140
Radio Spectrum Management
0.0301477514
Rakon Ltd.
0.0249346566
Rangiora New Life School
0.0360664993
Rape Prevention Education-Whakatu Mauri
0.0535592138
Rauawaawa Kaumatua Charitable Trust
0.0535687972
Raukatauri Music Therapy Centre
0.0249346566
Raukura Hauora O Tainui Trust
0.0226848532
Rayonier New Zealand Ltd
0.0269223989
Refugees as Survivors New Zealand
0.0357429619
Reid Construction Systems Ltd
0.0397538552
Renewable Energy
0.0069284140
Repromed
0.0992710506
Reserve Bank of New Zealand
0.0790194846
Resilient Organisations
0.0397538552
Resource Teacher: Learning and Behaviour
0.0249346566
Revolution Fibres Ltd
0.0626623983
Riccarton Rotary
0.0000000000
Risk Strategies Research and Consulting
0.0170942902
Rivuli Development
0.0111840626
RML Engineering
0.0109051918
Roche Products Limited
0.0357429619
Rockwell Automation
0.0249346566
Rolleston Veterinary Clinic
0.0599621860
Ropata Village Medical Centre
0.0857164925
Rotorua General Practice Group
0.0461819574
Rowe Davies Research Ltd
0.0366550992
Royal Australian and New Zealand College of Psychiatrists
0.0249346566
Royal Forest and Bird Protection Society of New Zealand
0.0466907631
Royal New Zealand College of General Practitioners
0.1050767416
Royal New Zealand Plunket Society
0.0996706514
Royal Society of New Zealand
0.0635867235
Ruaimoko Productions and Consultancy Ltd.
0.0212473008
Rumenz Ltd
0.0305050676
RuralLink
0.0109051918
[ reached getOption("max.print") -- omitted 511 entries ]
$value
[1] 40.10482
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[1] 21top_10_eig1 <- tail(sort(eig1$vector), 10)
top_10_eig1 AgResearch Auckland District Health Board Canterbury District Health Board
0.3760716 0.4334652 0.4357203
University of Waikato AUT University Victoria University of Wellington
0.4373508 0.4700463 0.5846012
University of Canterbury Massey University University of Otago
0.5943213 0.6779365 0.8521192
University of Auckland
1.0000000 bottom_10_eig1 <- head(sort(eig1$vector), 10)
bottom_10_eig1 Alzheimers Northland AP EnerTec Ltd.
0 0
Aviation Industry Association of New Zealand Inc Bio Soil and Crop Ltd
0 0
Blues Rugby Club Bruce Shallard and Associates
0 0
ChangeMakers Refugee Forum Chatham Rock Phosphate Ltd.
0 0
Chilton Saint James School Crown Fibre Holdings Limited
0 0 eig2 <- eigen_centrality(net)
head(eig2)$vector
45 South Management Ltd.
0.0051405189
Abacus ALS
0.0231551697
AbacusBio Ltd.
0.0356973370
ABB Power Quality
0.0047352544
ABI Rehabilitation New Zealand Ltd.
0.0063161772
AC Research Associates
0.0387233559
Academic Colleges Group New Zealand
0.0230236317
Accident Compensation Corporation
0.0908018610
Action on Smoking and Health New Zealand
0.0092094527
Active Health
0.0325944350
Acurity Health Group ltd.
0.1227547002
Ade Consultants
0.0460472634
Adidas Sports Medicine
0.0230236317
Adis International Ltd.
0.0192535471
Advanced Clinical Skills Centre
0.0568509437
AECOM
0.0462858055
AECS Ltd.
0.0087353529
Aerocool Ltd.
0.0043676764
Aeroqual Ltd.
0.0417272451
Affinity Services
0.0460472634
AFT Pharmaceuticals Ltd
0.0447142640
AFTpharmaceuticals
0.0460472634
Agencies for Nutrition Action
0.0323759262
Agile Utilities New Zealand Ltd
0.0186176938
Agknowledge Ltd.
0.0138076338
AgResearch
0.1295355263
Agri-Optic NZ Ltd.
0.0186176938
Agribusiness Group
0.0357889155
AgriGenesis Biosciences Ltd
0.0155277450
AgriHealth NZ Limited
0.0003791672
Agrimm Technologies Ltd
0.0014114278
AgriNova NZ Ltd
0.0034342151
AgriQuality Limited
0.0024519060
Agvance Marketing Ltd.
0.0122912251
Air New Zealand
0.0448256895
Air Quality Ltd.
0.0479686889
Airborne Honey Ltd.
0.0178906864
Akaroa Medical Centre
0.0308851034
Ako Aotearoa National Centre for Tertiary Teaching Excellence
0.0033343580
Akoranga Integrated Health Clinic
0.0091741574
Alan Bell and Associates
0.0150891395
Albany Basin Accident and Medical Centre
0.0057390827
Alcohol Advisory Council of New Zealand
0.0033898578
Alcohol Harm Minimisation Advisory Group
0.0188806358
Alcohol Healthwatch Trust
0.0460472634
Alexandra Lions Club
0.0054840206
Alexandra Medical Centre
0.0308851034
Alfriston College
0.0087353529
All Seasons Pharmacy
0.0460472634
Allan Planning and Research Ltd.
0.0072615978
Allen & Clarke Policy and Regulatory Specialists Limited
0.0697992842
Alphalabs
0.0118676988
Alpine and Polar Processes Consultancy
0.0340824367
Alzheimers Northland
0.0000000000
Amalgamates Solutions and Research Ltd.
0.0076372971
Amity Health Centre
0.0308851034
Ancare New Zealand Ltd.
0.0154425517
Ancare Scientific Ltd
0.0148012613
Anexa FVC
0.0247029116
Anglesea Medical Properties Ltd
0.0630087470
Animal Dermatology NZ
0.0087018909
Animal Health Board New Zealand
0.0152942973
Animals and Marine Surveillance and Investigation Team
0.0186176938
Animation Research Limited
0.0308851034
Antarctic Heritage Trust
0.0087353529
Antarctica New Zelaand
0.0599199499
Antarctica Scientific Limited
0.0133450945
Antipodean Pharmaceuticals
0.0514852405
Aorangi Veterinary Services
0.0023364362
Aotea Pathology Ltd.
0.0798343978
Aotearoa Alcohol and Other Drug Consumer Network
0.0393726856
AP EnerTec Ltd.
0.0000000000
Applied Engineering Research Ltd.
0.0039634640
Applied Research and Technologies Ltd.
0.0062097830
Applied Research Associates New Zealand
0.0071538796
AquaBio Consultants Ltd.
0.0081432486
Aquaculture New Zealand
0.0426818114
Aqualinc Research Ltd.
0.0690067072
Aquanet Consulting Ltd.
0.0186176938
Aquatic Research Solutions Ltd.
0.0237424298
Aranui High School
0.0077470596
ARANZ Geo Ltd
0.0071538796
ARANZ Medical Scanning
0.0083697771
Areograph Ltd.
0.0332527306
ARH Construction
0.0460472634
Aroa Biosurgery
0.1138977058
Arohanui Hospice
0.0011343690
Arotec Diagnostics Ltd.
0.0186770932
Ascot Angiography
0.0263744519
Ascot Women's Cancer Centre of New Zealand
0.0017815247
Asia New Zealand Foundation
0.0602268311
Asphalt Products Limited
0.0071028817
Aspiring Veterinary Service Ltd
0.0211938675
ASR Limited Martine Consulting and Research
0.0274945136
Assa Abloy New Zealand Ltd
0.0308851034
Assistive Technology Ltd.
0.0186176938
Assurity Consulting Ltd
0.0045870787
AsureQuality
0.0362800019
AsureQuality Ltd.
0.0260401584
At the Vets
0.0197859118
Atkinson and Rapley Consulting
0.0093088469
Atlantis HealthCare
0.0460472634
Auckland-Waikato Fish and Game Council
0.0133374320
Auckland Astronomical Society
0.0562439578
Auckland Botanic Gardens
0.0382454773
Auckland Breast Centre
0.0057390827
Auckland City Mission
0.0825744675
Auckland Clinical Studies Ltd.
0.0769368983
Auckland Council
0.1164176955
Auckland Cricket Assn Inc
0.0091741574
Auckland Dermatology
0.0063161772
Auckland District Health Board
0.2346215489
Auckland Eye
0.0658220465
Auckland Heart Group
0.0400120643
Auckland Institute of Studies
0.0139155958
Auckland International Airport Limited
0.0091741574
Auckland Museum
0.0656154014
Auckland Refugee Community Coalition
0.0460472634
Auckland Regional Council
0.0460472634
Auckland Southern Cross Hospital Group
0.0123172631
Auckland Transport
0.0460472634
Auckland Zoo
0.1057470228
Aurecon
0.0344279915
Australian and New Zealand College of Anaesthetists
0.0338273120
AUT University
0.1992334997
Automation Design Ltd
0.0030373531
Aviation Industry Association of New Zealand Inc
0.0000000000
Avivet Ltd
0.0152736034
Avocado Industry Council
0.0049038121
Babbage Consulting Ltd.
0.0703392860
Ballance Agri-Nutrients Limited
0.0332383217
Bank of Scotland
0.0460472634
Bartonk Solutions
0.0055011600
Batten Animal Research Network
0.0210882627
Baxter Healthcare Limited
0.0839797666
Bay Audiology
0.0047352544
Bay of Plenty District Health Board
0.0747680534
Bay of Plenty Polytechnic
0.0747402583
Bay of Plenty Regional Council
0.0378856517
Bay Urology
0.0171981126
Bayer CropScience New Zealand
0.0061878771
Bayleys Property Services
0.0460472634
BC Consulting Ltd.
0.0032060228
BCRL Energy Limited
0.0013166712
Beca
0.0782501365
Beef and Lamb New Zealand
0.0995252040
Bennett Scientific
0.0488886893
Benthic Science Ltd.
0.0227041495
Berryworld Ltd
0.0083411103
Best Practice Advocacy Centre
0.0504594210
Beta Solutions
0.0646649572
Bethesda Care
0.0287627144
Betta Bees Research Ltd
0.0308851034
Better Border Biosecurity
0.0103878326
BHU Future Farming Centre
0.0198514744
Bickler Consultants Ltd.
0.0395269924
BikeNZ
0.0142057633
Bio Soil and Crop Ltd
0.0000000000
Bioactives Research New Zealand
0.0393679157
Biodiscovery New Zealand Ltd.
0.0230018794
Biomarine Ltd.
0.0460472634
Biomatters Ltd.
0.0539087351
Biometrics Matters Ltd
0.0358754961
Biopolymer Network Ltd
0.0554100925
Biosecurity New Zealand
0.0295484208
BioSylve Forest Science NZ Ltd.
0.0039634640
BirdLife Global Seabird Programme
0.0068979961
Blind Foundation
0.0186176938
BLIS Technologies Ltd.
0.0279561405
Blue Water Marine Research
0.0533088612
Blues Rugby Club
0.0000000000
Bodeker Scientific
0.0499122626
Body Aid Clinic Ltd
0.0308851034
Boffa Miskell Ltd
0.0990145387
Bomac Laboratories Ltd
0.0478457679
Boulcott Hospital
0.0031020184
Braemar Hospital
0.0448036136
BRANZ Ltd.
0.0510072266
Bream Bay Medical Centre
0.0460472634
Breast Care and Screening Services
0.0523634406
Breast Surgeons' Society of New Zealand
0.0460472634
Breen Consulting
0.0145900217
Brian Ricketts Geological Consulting Limited
0.0041457636
Broadway Medical Centre
0.0524416958
Broadway Surgical Clinic
0.0109319084
Broken Hills Gold Co
0.0460472634
Brownrigg Agriculture
0.0023271531
Bruce Shallard and Associates
0.0000000000
Bunnythorpe School
0.0054840206
Cadwallader Tree Consultancy
0.0142057633
Cahill Animal Hospital
0.0062058979
CAL Engineering Management
0.0115436866
Callaghan Innovation
0.0517685982
Cambridge Clinic
0.0448372632
Cambridge Veterinary Services
0.0087018909
Cameron Medical Clinic
0.0565380297
Campbell and Associates Ltd.
0.0049038121
Cancer Control Council of New Zealand
0.0594165628
Cancer Society of New Zealand
0.0749738175
Canterbury Charity Hospital Trust
0.0264206800
Canterbury Civil Defence and Emergency Management Group
0.0112893326
Canterbury District Health Board
0.2127478630
Canterbury Earthquake Recovery Authority
0.0384436631
Canterbury Health Ltd
0.1072507642
Canterbury Medical Imaging
0.0197291540
Canterbury Museum
0.0580257823
Canterbury Rugby Football Union and Crusaders
0.0083462461
CanZealand Geoscience Ltd
0.0065392413
Cape Kidnappers and Ocean Beach Wildlife Preserve
0.0482699631
Cape Sanctuary
0.0558745263
Capital and Coast District Health Board
0.1253997379
Capital Eye Specialists
0.0045629517
Capital Research
0.0366594181
Carbon Partnership
0.0054840206
Cardiac Inherited Disease Group
0.0568509437
Care of Orca Research Trust
0.0002863718
Carey Baptist College
0.0460472634
Carroll Consulting ltd
0.0210014960
Carson Associates Ltd.
0.0039634640
Carter Holt Harvey Ltd.
0.0510266532
Carter National Observatory
0.0298089593
Cashmere Health
0.0158064741
Catch Ltd.
0.0460472634
Catmed
0.0044210020
Cawthron Institute
0.0946198276
CBG Health Research Limited
0.0786848279
Centennial Health
0.0340179725
Center for Backyard Astrophysics
0.0003316279
Central and Southern New Zealand Craniofacial Program
0.0473512653
Central City Vets
0.0065054564
Central Otago Tourism
0.0308851034
Central Stories Museum
0.0018280069
CentralMed
0.1051324223
Centre for Backyard Astrophysics
0.0057098871
Centre for Clinical Research and Effective Practice
0.0514017654
Centre for Dairy Excellence
0.0195163691
Centre for Minerals Environmental Research (CMER)
0.0322017746
Centre for Research Evaluation and Social Assessment
0.0024621169
Centre for Youth Health in South Auckland
0.0294180641
CH and Associates
0.0199705401
ChangeMakers Refugee Forum
0.0000000000
Chatham Rock Phosphate Ltd.
0.0000000000
Chemipreneur Ltd.
0.0332762804
Chemistry Communications
0.0287627144
Chiefs Super Rugby Franchise
0.0315897884
Child and Youth Health
0.0356827065
Child Poverty Action Group
0.0460472634
Chilton Saint James School
0.0000000000
Chiptech Ltd
0.0323759262
Christchurch City Council
0.0890595871
Christchurch Emergency Care Foundation
0.1004482890
Christchurch Polytechnic Institute of Technology
0.0586470274
Christchurch Psychologists' Office
0.0450908667
Christchurch Vascular Group
0.0418158369
City Care Ltd
0.0142057633
City Fitness
0.0552771119
Civil Aviation Authority
0.0323324786
Claro
0.0460472634
ClearSight Consultants Ltd
0.0726772875
Clement and Associates Ltd
0.0114933824
Clendon Burns and Park Consulting Engineers
0.0099684125
CLIMsystems Ltd.
0.0043676764
Clinical Horizons
0.0440184504
Clinical Systems
0.0063944324
Clutha Veterinary Association
0.0332215396
Coast and Catchment Ltd
0.0404210536
Coast to Coast Health Centre
0.0057390827
Coastal and Aquatic Systems Ltd
0.0740056293
Coastal Systems (NZ) Ltd.
0.0046167379
Coastline Consultants
0.0039634640
Cognition Education Limited
0.0153490878
Cognosco
0.0161886645
Colgate-Palmolive Ltd
0.0142057633
Colin Christian Ltd.
0.0308851034
Collins Carriers Ltd.
0.0056457110
Colmar Brunton
0.0460472634
Columba College
0.0308851034
Common Ground Ltd
0.0274942182
Commtest Instruments Ltd
0.0142057633
Community Clinic for Sexual Health and Contraception
0.0460472634
Compac Sorting Equipment Ltd.
0.0509510755
Compac Technologies
0.0186176938
Compass Health
0.0279327199
Compusoft Engineering Limited
0.0460472634
Compusoft Engineering Ltd.
0.0251974095
Comtel System Ltd.
0.0192843263
Comvita New Zealand Ltd.
0.0229004554
Connectos Consulting
0.0608228747
Connovation Ltd.
0.0484272023
Conservation and Environmental Management
0.0176382812
Construction Techniques Ltd.
0.0602530267
Consulting Dietitians Ltd.
0.0338273120
Contact Energy Ltd.
0.0133479861
Contract Landscapes Ltd
0.0046167379
CORE Education Ltd.
0.0259354160
Cosgrove
0.0142057633
Counties Manukau District Health Board
0.1388667186
Covec Ltd
0.0797552223
CPG New Zealand Ltd.
0.0186176938
Crawford Medical Centre
0.0251974095
CRL Energy Ltd.
0.0285939087
Cromwell College
0.0133374320
Cropmark Seeds Limited
0.0148377240
Crown Fibre Holdings Limited
0.0000000000
CURT St George's Medical Centre
0.1088339740
Cuttriss Consultants Ltd
0.0065392413
Cymbiotix Group Limited
0.0552214209
Cyperus Ltd
0.0681144984
Dairy Consultants Ltd.
0.0032826090
Dairy Goat Co-operative (NZ) Ltd.
0.0465849078
Dairy Production Systems Ltd.
0.0002752443
DairyNZ
0.0784106113
David Butler Associates Ltd
0.0186176938
Davidson Environmental Ltd.
0.0819055933
DaVinci Clinic
0.0019976835
DCM Process Control Ltd.
0.0460472634
DEA Research Software Surgery Ltd.
0.0460472634
Deepwater Group Ltd
0.0114933824
DeerNZ
0.0049038121
Deloitte
0.1097558239
Department of Conservation
0.1478014695
Department of Corrections
0.0142057633
Development Action
0.0133374320
Development By Design
0.0133374320
Devon Medical Centre
0.0049977405
DHI Water and Environment
0.0041031253
Diabetes Otago Inc
0.0308851034
Diagnostic Laboratory
0.0402217443
Diagnostic Medlab
0.0576565345
Digestive Health Services
0.0406815603
Digital Sensing Limited
0.0197948985
Disability Connect
0.0482699631
Disability Resource Centre
0.0608228747
Diversity NZ
0.0608228747
DM Consultants
0.0636283979
DNA Investments Ltd.
0.0044249022
Dnature diagnostics and research Ltd.
0.0604438840
Doctors for Sexual Abuse Care
0.0098038017
Donaghys Industries
0.0051405189
Donald Beasley Institute
0.0513084063
Dorothy-Jean and Associates
0.0059029423
Dovedale Ltd.
0.0862412137
Downer EDI Works Limited
0.0127183613
Dr. Malcolm McKellar Ltd.
0.0026601840
Dragonfly Ltd.
0.0398691754
Drummond Food Science Advisory Ltd.
0.0308851034
Dumpark Data Science
0.0005298051
Duncan Cotterill
0.0175662940
Dunedin City Council
0.0334516992
Dunedin Heat Pumps Limited
0.0308851034
Dunedin South Veterinary Clinic
0.0186176938
Dunning Thornton Consultants Ltd.
0.0506640013
Dynamic Controls Ltd.
0.0141326860
Dynatest
0.0519614827
Dyspraxia Support Group of New Zealand
0.0406815603
Earthquake Commission
0.0774697252
Earthtech Consulting Limited
0.0482699631
Eastern Institute of Technology
0.1029689503
Eastern Region Fish and Game
0.0119179126
Eastern Suburbs Association Football Club (ESAFC)
0.0646649572
Eastland Veterinary Services Ltd.
0.0209541299
Eaton Power Quality Ltd.
0.0035514408
ECG Consultants
0.0186176938
Eco-Vista Photography and Research Ltd.
0.0675821239
Eco Nomos Ltd.
0.0132263543
Eco Research Associates Ltd
0.0840869064
ECoast Limited
0.0115056815
EcoGecko Consultants Ltd.
0.0410698575
Ecosynergy Group Ltd (EGL)
0.0133374320
Ectus Ltd
0.0087353529
Edmund Lawler and Associates Limited
0.0133374320
Education House
0.0000000000
Education Review Office
0.0460472634
Educational Leadership Project
0.0087353529
Electricity Authority
0.0575959558
Eli Lilly and Company (New Zealand) Limited
0.0549214843
Elmwood Orthopaedics
0.0332350417
Eltham District Veterinary Services
0.0218472177
Endoscopy Auckland
0.0485546450
Energy Efficiency and Conservation Authority
0.0587375573
Energy Solution Providers Ltd.
0.0056457110
EnForm Tech
0.0108447368
Enigma Publishing Ltd.
0.0552493766
Ensys Ltd
0.0071028817
Entecol Ltd.
0.0364694794
Enviro-Mark Solutions Ltd.
0.0142057633
Enviro Research
0.0062526751
Environment Canterbury
0.1051682495
Environment Protection Authority(EPA)
0.0251870864
Environmental Management Services
0.0065392413
Environmental Restoration Ltd
0.0039634640
ENZO Nutraceuticals Limited
0.0432330434
Epi-interactive
0.0467923996
Epsom Girls Grammar School
0.0230236317
Equine Health Association
0.0044249022
ERA Ecology
0.0570685119
Erin Park
0.0387233559
ESR
0.1281931180
Etec Crop Solutions
0.0049038121
Eudyptes EcoConsulting Ltd
0.0376909566
Explore NZ
0.0186176938
Eye Institute
0.0568509437
Far North District Council
0.0252433140
Farm Cove Observatory
0.0130408739
Feilding Medical Centre
0.0617973474
FEM Ltd.
0.0000000000
Fern Research Foundation
0.0151686834
Ferndale School
0.0142057633
Fertility Associates
0.0467351163
Financial Markets Authority
0.0133374320
Fish and Game NZ
0.0195336557
Fisher and Paykel Appliances
0.0460472634
Fisher and Paykel Healthcare Ltd.
0.1051717710
Fishing Vessel Management Services Ltd.
0.0106868995
FitzRoy of Merivale
0.0196897839
Fletcher Construction Co
0.0525226591
FMR GROUP LTD
0.0062108748
Fonterra
0.0781241575
Food and Bio-based Products Group
0.0139258291
Food and Health Group
0.0201774155
Foot Science International Ltd.
0.0308851034
Forensic and Industrial Science Ltd
0.0230236317
Forest and Bird
0.0635109105
Forever Beech Ltd.
0.0142057633
Foundation for Arable Research
0.0087407843
Foundation for Research Science and Technology
0.0186176938
Fox and Associates-Consulting Surveyors
0.0207450047
Fred Hollows Foundation
0.0542152213
Fresenius Medical Care Australia Pty Ltd (New Zealand Branch)
0.0524416958
Freshport NZ Ltd
0.0056457110
Frontier Global Ltd.
0.0460472634
Fruitfed Supplies
0.0033567474
Fruition Horticulture
0.0213326267
FullSpectrum Ltd.
0.0087353529
Fulton Hogan Ltd.
0.0281771669
Future Forests Research
0.0039634640
Future Steps
0.0911381301
FuturebyDesign Ltd.
0.0642077847
FutureMATH Ltd.
0.0009506246
Gallagher Animal Management Systems
0.0087353529
Gambling Helpline
0.0277918512
Genesis Research & Development Corporation Ltd
0.0231170956
Genetic Technologies Ltd.
0.0093088469
Gentrack Limited
0.0160421358
Geoenvironmetal Services
0.0018063002
GEOKEM
0.0226834386
Geomarine Research
0.0605650560
Geoscience Consulting Ltd
0.0460472634
Geotech Consulting Ltd
0.0191586936
Geothermal Engineering Ltd
0.0460472634
Geoventures Limited
0.0308851034
GF McLaren Research Limited
0.0051405189
GHD Centre Level Napier St.
0.0460472634
GHD Limited
0.0000000000
Gillies McIndoe Research Institute
0.0685261438
Gisborne District Council
0.0099684125
Glass Earth Gold Ltd
0.0308851034
Glenview Medical Centre
0.0317386789
Global Action for Health Equity Network (HealthGAEN)
0.0093088469
Global Public Health Company Ltd
0.0429321509
GNS Science
0.1420115084
Golden Bay Cement
0.0472075352
Golder Associates (NZ) Ltd
0.0692849438
Good Life Research Centre Trust
0.0135366442
Google
0.0133374320
Greater Wellington Regional Council
0.0457159187
Green Lane Hospital
0.0028695413
Greenweaver Architecture Ltd
0.0156861752
Greerton Early Childhood Centre
0.0229411162
Gribbles Veterinary
0.0507399571
GroPlus Ltd.
0.0000000000
Ground Investigation Ltd
0.0460472634
Growth Solutionz
0.0000000000
Guardian Health Care (Bupa)
0.0387233559
Hagley Community College
0.0142057633
Hally Labels
0.0066687160
Hamilton Eye Clinic
0.0460472634
Hamilton Sacred Heart College for Girls
0.0087353529
Hamilton Veterinary Services
0.0186176938
Hamilton Zoo
0.1173253833
Hanham Consultants
0.0460472634
Hanmer Clinic Tauranga
0.0308851034
Hapai Te Hauora Tapui Ltd
0.0321977891
Harker Underground Construction Limited
0.0148914750
Harris Consulting
0.0162637073
Hauora Heretaunga
0.0230236317
Hauora Waikato Group
0.0341433236
Hauraki Maori Trust Board
0.0478494123
Hawke's Bay Alcohol and Drug Service
0.0502157132
Hawke's Bay District Health Board
0.0825730299
Hawke's Bay Regional Council
0.0898103766
Hawkins Watts
0.0460472634
Health Alliance
0.0511753810
Health Care Aotearoa
0.0142057633
Health New Zealand Ltd.
0.0708903950
Health Outcomes Associates Ltd.
0.0115118159
Health Partners Consulting Group
0.0351941802
Health Promotion Agency
0.0472086837
Health Quality and Safety Commission
0.0426432777
Healthscope Laboratories
0.0042799012
HealthWEST
0.0544847716
Heart Foundation of New Zealand
0.0436981418
Heavy Engineering Research Association
0.0610023788
HEB Construction
0.0016618379
Heinz Wattie's
0.0240575111
Heke Consulting
0.0460472634
Helios Integrative Medical Centre
0.0000000000
Hemptech
0.0017470706
Henderson Medical Centre
0.0871226265
Henderson Valley Primary School
0.0043676764
Hepatitis Foundation of New Zealand
0.0306492934
Herbert Morton Accountants
0.0087353529
Heretaunga Health
0.0568509437
Heritage New Zealand Pouhere Taonga
0.0460472634
High Performance Sport New Zealand
0.0153035150
Highnam Associates Ltd.
0.0460472634
Hill Laboratories Ltd.
0.0828994823
Hiway Geotechnical
0.0460472634
HodderBalog Social and Scientific Research
0.0133374320
Holcim (NZ)
0.0000000000
Holmes Consulting Group
0.0484128920
Holmes Fire and Safety
0.0542249472
Horizons Regional Council
0.0770189360
Horowhenua Community Practice
0.0308851034
Horowhenua Library Trust
0.0000000000
Horteye Ltd
0.0052878974
HortPlus
0.0082835804
Hospice New Zealand
0.0898956980
Hospice Palliative Care Education
0.0561542191
Hospice Waikato
0.0520958214
Hot Solutions Ltd.
0.0301775113
Humes Pipeline Systems
0.0460472634
Huntly Community Link
0.0000000000
Hurricanes Rugby
0.0140779695
Hush Interiors Ltd
0.0142057633
Hutt Valley District Health Board
0.0673659665
Hyland Consultants
0.0161885984
Hyland Fatigue Earthquake Engineering
0.0644929599
Hyperbaric Health
0.0465535405
IAG
0.0142057633
Ian Kusabs and Associates Limited
0.0079984753
Ian McLean Consultancy Services Ltd.
0.0460472634
Ichthyo-niche
0.0518967199
IGENZ Ltd
0.0602845735
ILR
0.0230413217
Immunisation Advisory Centre
0.0338273120
Inclusive Education Action Group
0.0482699631
Independent Petroleum Laboratory
0.0509510755
Indufor Asia-Pacific Ltd
0.0049398258
Infoics Limited
0.0061103089
Inform Planning Ltd
0.0574269711
Infrastructure Decisions Limited
0.0393626984
Inglewood Veterinary Services
0.0222282878
Injury Prevention Aotearoa
0.0660251011
Inland Revenue
0.0257889962
Innate Immunotherapeutics Limited
0.0931790663
Innate therapeutics
0.0154421679
Inner City Women's Group
0.0460472634
Inner Zest Ltd.
0.0460472634
INR Online Ltd
0.0049977405
Insect Science Solutions
0.0122937041
Insights MSD
0.0046253362
Inspiring Ltd.
0.0407808998
Institution of Professional Engineers New Zealand
0.0472907888
Intellectual Property Office of New Zealand
0.0155277450
Intensive Care Flight Paramedic
0.0191338345
Interactionz
0.0087353529
InterAg
0.0861891581
International Animal Welfare Consultants Limited
0.0186176938
International Earth Sciences IESE Ltd.
0.0659239368
International Pacific College
0.0093088469
International Student Ministries of New Zealand
0.0336583841
International Telematics Ltd.
0.0214318693
Interpine
0.0050900946
Interpine Forestry Ltd
0.0138258900
Intus Digestive and Colorectal Care
0.0308851034
Invenco Group Ltd.
0.0230236317
Investigation Geology Ltd
0.0148914750
IPENZ
0.0347291376
Irrigation New Zealand Inc.
0.0094207704
Isolytix
0.0308851034
IZON Science Ltd.
0.0771616876
Jackett Consulting
0.0029701530
Jacobs Engineering
0.0525226591
Jade Software Corporation
0.0450908667
James and Monroe
0.0277918512
JMR Distributors Ltd
0.0093088469
John Jones Steel
0.0628391701
John Wood Consulting
0.0609976234
Johne's Management Limited
0.0300664708
Jowett Consulting Ltd.
0.0200443288
JRA (NZ) Ltd.
0.0230236317
Julian King and Associates Limited
0.0165427629
Ka Mau Te Wero
0.0054840206
Kaikorai Valley College
0.0308851034
Kaikoura Ocean Research Institute Inc.
0.0528531166
Kaipaki Veterinary Services
0.0186176938
Kaipara District Council
0.0252433140
Kapiti Coast District Council
0.0230749117
Karori Sanctuary Trust
0.0292948357
Katoa Ltd
0.0724488544
Kea Conservation Trust
0.0160975229
KEA Consultant
0.0000000000
Keratec Ltd.
0.0184249299
Kidney Health New Zealand
0.0802779436
Kina Families and Addictions Trust
0.0533050592
Kinetic Engineering Design
0.0460472634
Kingdom Clinic
0.0366216848
Kiwi Well Evaluation Ltd
0.0442225354
Kiwi Wildlife
0.0018312513
Kiwicap Research Ltd
0.0000000000
Kiwikiwi Research and Evaluation Services
0.0040502530
Kono Horticulture Limited
0.0357889155
Koru Environmental Consultants Ltd
0.0116185819
Koti Technologies
0.0071028817
Kumeu Observatory
0.0056254637
Kurahaupo Consulting
0.0027420103
KVB Kunlun New Zealand Limited
0.0093088469
Labtests
0.0386890460
Lake Hawea Institute of Cryodynamics
0.0275431954
Lakes District Health Board
0.0684553187
Land Information New Zealand
0.0358547024
Landcare Research
0.1190954716
Landcorp Farming Limited
0.0679286984
Langimalie Clinic
0.0134638642
LanzaTech NZ Ltd.
0.0348485674
Lassey Research and Education Ltd
0.0072615978
Lateral Technology
0.0460472634
Laura Fergusson Trust
0.0357833318
Law Commission
0.0133374320
LeaderBrand Produce Ltd.
0.0050583811
Learning for Sustainability
0.1004878852
Leather & Shoe Research Association of New Zealand
0.0114880932
Leinster Orthopaedic Centre
0.0039249764
Levare Limited
0.0338273120
Levin and Horowhenua Veterinary Centre
0.0193135951
Lewis and Barrow Ltd.
0.0115436866
LIC
0.0346966900
Life Technologies Ltd.
0.0142057633
LightBox Psychology Services
0.0450908667
Lincoln Agritech Ltd.
0.0659616412
Lincoln University
0.1226068740
Lincolne Scott Ltd.
0.0142057633
Lindis Consulting
0.0102237471
Linnaeus Laboratory
0.0150304276
Litmus
0.0688547975
Livestock Solutions and Services
0.0093088469
Living Cell Technologies NZ Ltd.
0.0217435202
Local Government New Zealand
0.0326537515
Logjiztix Ltd
0.0053969097
Lowe NZ
0.0072615978
Lucas Industries (NZ) Ltd.
0.0460472634
LWT Animal Nutrition Ltd.
0.0065054564
MacMurray Hypertension Clinic Ltd
0.0517863461
MAGAK
0.0041457636
Magic Sparks Early Learning and Development Centre
0.0556438221
Magritek Limited
0.0482701687
Makoura College
0.0133374320
Malaghan Institute of Medical Research
0.0228228645
Male Survivors of Sexual Abuse Trust
0.0142057633
Manaaki Te Awanui
0.0762835390
Manaia Health Primary Health Organisation
0.0149132401
Manawatu Diagnostics
0.0093088469
Mangere Community Health Trust (Primary Health Organisation)
0.0402184964
Manukau Institute of Technology
0.0611149351
Manukau SuperClinic
0.0230236317
Manurewa South School
0.0460472634
Maori Hill Clinic
0.0308851034
Maori Pharmacists Association
0.0322411474
Maramatanga Consultants Ltd
0.0186176938
Marine Fisheries Research Services Limited
0.0019038246
Marine Wildlife Research Ltd
0.0300890610
Marinoto Clinic
0.0237505243
Mark L Batchelar Consulting Engineers
0.0142057633
Market Economics Ltd.
0.0037235388
Marlborough Wine Research Center
0.0816328366
MARS Bioimaging Ltd
0.0213386082
Marshall Day Acoustics Ltd.
0.0606549382
Mary Potter Hospice
0.0191829319
Massey University
0.4043170510
Masters Consulting Ltd.
0.0038076492
Matakina Technology Ltd
0.0310254924
Matamata Medical Centre
0.0534729471
Matamata Veterinary Services Ltd
0.0095729499
MBCentury Ltd
0.0460472634
McConnell Dowell Constructors Ltd.
0.0024310037
McLaren Research Ltd.
0.0049038121
McManus Geotech Ltd.
0.0160012959
Medical Council of New Zealand (MCNZ)
0.0044368199
Medical Research Institute of New Zealand
0.0959002698
Medlab Central
0.1074201462
Melanoma Unit
0.0170362828
Member International Neuropsychological Society
0.0308851034
Mental Health Education Resource Centre
0.0142057633
Mental Health Foundation of New Zealand
0.0673658772
MercyAscot Hospitals
0.0544523484
Meridian Energy Ltd.
0.0257894343
Mesynthes Ltd.
0.0511926836
Meteorological Service of New Zealand Ltd.
0.1300676576
Methanex
0.0105523723
MetOcean Solutions Ltd.
0.0488204377
Microfossil Research Ltd
0.0392270901
MidCentral District Health Board
0.0985395366
Midland MRI
0.0087353529
Midland Regional Forensic Services
0.0460472634
Midlands Health Network
0.0240949507
Midwifery Council of New Zealand
0.0425781588
Mighty River Power Ltd.
0.0341184291
Millar Instruments
0.0138142156
Milton Health Centre
0.0340179725
Ministry for Primary Industries
0.0960947927
Ministry for Primary Industry
0.0514841332
Ministry for the Environment
0.1382364489
Ministry of Business Innovation and Employment
0.0655398283
Ministry of Civil Defence and Emergency Management
0.0157063839
Ministry of Education
0.0852927768
Ministry of Foreign Affairs and Trade
0.0225411443
Ministry of Health
0.1113663921
Ministry of Justice
0.1089290995
Ministry of Pacific Island Affairs
0.0831390961
Ministry of Social Development
0.0890037911
Ministry of Transport
0.0140820287
Mission Heights Primary School
0.0019038246
MLB Consulting Engineers
0.0142057633
Molehill Astronomical Observatory
0.0134405510
Moorhouse Medical Clinic
0.0062185157
Morrison Consultants Ltd
0.0082018496
Motu Economic and Public Policy Research
0.0686432781
Mountains to Sea Conservation Trust
0.0691552784
MSD Animal Health Ltd
0.0135585589
Mt. Albert Psychological Services Ltd
0.0029500157
Mulgor Consulting Ltd.
0.0143306442
Muscular Dystrophy Association of New Zealand
0.1034877988
MWH New Zealand Ltd
0.0301265134
N-Squared Software
0.0363610637
NaeNae Medical Centre
0.0092387159
National Addiction Centre
0.0308851034
National Association of Steel-Framed Housing Inc
0.0244281280
National Council of Women of New Zealand
0.0095547877
National Heart Foundation of New Zealand
0.0609738915
National Library of New Zealand Te Puna Matauranga O Aotearoa
0.0134745407
National Maori Health Workforce Organisation
0.0308851034
Natural Resource Assessors
0.0469826263
Needle Exchange Programme NZ
0.0393726856
Nelson Forests Limited
0.0181692274
Nelson Marlborough District Health Board
0.0740128398
Nelson Marlborough Fish and Game
0.0197995358
Nelson Marlborough Institute of Technology
0.1117490881
Nelson Marlborough Regional Council
0.0274942182
Neonatal Intensive Care Unit
0.0154425517
NetSafe
0.0230236317
NetValue
0.0000000000
Neuren Pharmaceuticals
0.0460472634
Neurological Foundation of New Zealand
0.0230236317
New Brighton Health Care
0.0211311771
New Image Group Ltd
0.0230236317
New River Ltd
0.0323759262
New Zealand Academy of Sport
0.0901702652
New Zealand Aerial Mapping
0.0538145960
New Zealand Agricultural Greenhouse Gas Research Centre
0.0172747246
New Zealand Agriseeds Limited
0.0235215058
New Zealand AIDS Foundation
0.0142059185
New Zealand Aluminium Smelters Limited
0.0460472634
New Zealand Antarctic Institute
0.0142057633
New Zealand Arable
0.0037924911
New Zealand Association of Optometrists
0.0319551258
New Zealand Avocado Growers Association
0.0049038121
New Zealand BioSecure Entomology Laboratory Research
0.0258852552
New Zealand Blood Service
0.0577707289
New Zealand Brain Research Institute
0.0514919843
New Zealand Breast Cancer Foundation
0.0357833318
New Zealand Centre for Conservation Medicine (NZCCM)
0.0655511273
New Zealand Climate & Health Council
0.0769323668
New Zealand College of Chiropractic
0.0260816842
New Zealand College of Midwives
0.0969724688
New Zealand Cot Death Association
0.0472075352
New Zealand Council for Educational Research (NZCER)
0.0310393467
New Zealand Defence Force
0.0563014817
New Zealand Dental Association
0.0329105832
New Zealand Employment Service and Work and Income New Zealand
0.0006555265
New Zealand Familial Gastrointestinal Cancer Service
0.0703012832
New Zealand Forestry Ltd
0.0046001084
New Zealand Geotechnical Society Ine (NZGS)
0.0000000000
New Zealand Guidelines Group
0.0643404183
New Zealand Gynaecological Cancer Foundation
0.0441224178
New Zealand Heart and Lung Transplant Service
0.0578435359
New Zealand Heavy Engineering Research Association
0.0233412811
New Zealand Homebased Early Childhood Education Association
0.0347296181
New Zealand Institute for Plastic and Cosmetic Surgery
0.0308851034
New Zealand Institute of Community Health Care
0.0466567796
New Zealand Institute of Economic Research
0.0457759701
New Zealand Institute of Medical Laboratory Science
0.0221871944
New Zealand Institute of Rural Health
0.0769323668
New Zealand Kiwi Foundation
0.0460472634
New Zealand Medical Association
0.0282584118
New Zealand Medical Students' Association
0.0614898151
New Zealand National Eye Bank
0.0108266365
New Zealand National LCP Office
0.0590795036
New Zealand Needle Exchange Programme
0.0349489208
New Zealand Nurses Organisation
0.0796368193
New Zealand Olympic Committee
0.0308851034
New Zealand Organisation for Rare Disorders (NZORD)
0.0308851034
New Zealand Parliament
0.0133374320
New Zealand Police
0.0726437977
New Zealand Qualifications Authority
0.0133374320
New Zealand Refining Co. Ltd.
0.0142057633
New Zealand Rheumatology Association
0.0941304794
New Zealand Rugby Union
0.0196939158
New Zealand School Acupuncture and Traditional Chinese Medicine
0.0142057633
New Zealand School of Music
0.0026674864
New Zealand Seafood Industry Council Ltd
0.0113485740
New Zealand Society for Earthquake Engineering (NZSEE)
0.0000000000
New Zealand Spinal Trust
0.0341505890
New Zealand Tertiary College
0.0206859733
New Zealand Timberlands Ltd
0.0007445967
New Zealand Transport Agency
0.0161702695
New Zealand Treasury
0.1004475808
New Zealand Underwater Heritage Group
0.0091570080
New Zealand Veterinary Pathology Ltd.
0.0151127618
New Zealand Winegrowers
0.0533088612
Newman Energy Research
0.0142057633
Newtown Medical Centre
0.0769323668
NextWindow Ltd
0.0769323668
Ngati Porou Hauora
0.0241349816
Ngati Whakaue Tribal Lands Inc
0.0039634640
Nielsen Company
0.0277520142
NIU Development Incorporated
0.0508154829
NIWA
0.1576987909
Norske Skog Tasman
0.0460472634
North Canterbury Veterinary Clinics
0.0212742619
North Shore Hospice
0.0384143907
North Shore International Academy
0.0273530466
Northcott Research Consultants Ltd.
0.0750651509
Northern Cancer Network
0.0207509279
Northern Region IDEA Services
0.0460472634
Northern Regional Alliance
0.0066771905
Northern Southland Veterinary Services
0.0034761237
Northland District Health Board
0.0879586046
Northland Regional Council
0.0934007545
NorthTec
0.0443143317
Novare Design Ltd.
0.0142057633
Numcore Ltd.
0.0460472634
Numinos Ltd.
0.0460472634
Nurse Maude Association
0.0275129369
Nutrigenomics New Zealand
0.0367598254
Nutrition Society of New Zealand
0.0154425517
NZ Oil and Gas
0.0198766733
NZ Parsa Tiling Limited
0.0142057633
NZFOCUS (NZ) Ltd.
0.0230236317
NZX Limited
0.0460472634
O'Kane Consultants (NZ) Ltd
0.0602226717
Oamaru Hospital
0.0154425517
Odyssey House
0.0230236317
Office of the Health and Disability Commissioner
0.0460472634
Office of the Parliamentary Commissioner for the Environment
0.0230406528
Omahu Urology Clinic
0.0366594181
OMV New Zealand Ltd.
0.0511029676
Oncology Surgery Ltd.
0.0408721696
Open Polytechnic of New Zealand
0.0834906228
OPRA Consulting Group
0.0142359485
Optimal Clinical Trials
0.0398952216
Opus International Consultants Ltd
0.0645022699
Oracle New Zealand
0.0133374320
Oral Health Centre
0.0416887837
Orange Consulting
0.0308851034
Orb Solutions
0.0529578883
Organ Donation New Zealand
0.0353269255
Oritain Global Ltd.
0.0308851034
Ornithological Society of New Zealand
0.0549868177
Orokonui Ecosanctuary
0.0442225354
OSPRI
0.0706606939
Otago Community Hospice
0.0476574625
Otago Computational Modelling Group Ltd.
0.0496956693
Otago Daily Times Collective
0.0308851034
Otago Girls High School
0.1088874926
Otago Museum
0.0553771184
Otago Polytechnic
0.0557382910
Otago Regional Council
0.0351789362
Otahuhu College
0.0581531258
Otakaro Pathways Ltd
0.0147002690
Otorohanga Dental Surgery
0.0308851034
OTRS Group Ltd
0.0602159741
Outome Management Services
0.0460472634
P.N. Plimmer and Associ.
0.0482699631
PA Handford and Assoc. Ltd.
0.0070008171
Pacific Brands
0.0230236317
Pacific Edge Biotechnology Ltd.
0.0998157607
Pacific Health Research and Development Foundation
0.0416413255
Pacific Radiology Group
0.0852379945
Pacific Women's Health Research and Development Unit
0.0683734936
Pakuranga Medical Centre
0.0033515457
Palaecol Research Ltd
0.0506475414
Palmerston North City Council
0.0101877423
Palmerston North City Library
0.0133374320
Pansophy Ltd
0.0220982646
Papamoa Pines Medical Centre
0.0928809741
Paraparaumu College
0.0523040361
Paric Limited
0.0460472634
Parkinson's New Zealand
0.0230236317
Parresia Research Limited
0.0460472634
Parsons Brinckerhoff
0.0460472634
Pasifika Horizon Healthcare
0.0460472634
Pasifika Medical Association
0.0516262885
Pasifika Research Ltd
0.0083367517
Pathlab
0.0433833264
Patients First
0.0191624112
Paton-Simpson Associates Limited
0.0400592608
Pattle Delamore Partners Ltd
0.0164941129
Pegasus Health Ltd
0.0642293445
Penny and Associates Ltd
0.0663179375
Perinatal and Maternal Mortality Review Committee
0.0707548700
Petersgate Counselling Centre
0.0142057633
PF Olsen and Company Ltd
0.0088351016
PGG Wrightson Seeds Ltd.
0.0258262532
PHARMAC
0.0438168198
Pharmaceuticol Ltd
0.0363256511
Pharmacy Guild of New Zealand
0.0460472634
PharmTech Service Limited
0.0396344015
Philosophy of Education Society of Australasia
0.0460472634
Photonz Corporation Ltd
0.0460472634
Pictor Ltd.
0.0460472634
Pingar Research
0.0047800509
Pinnacle Group Ltd
0.0508646209
PipeTechnologies
0.0525226591
Pipfruit New Zealand
0.0280166654
Planning Consultants Ltd
0.0574269711
Plant and Food Research
0.1064951902
Plant Protection Chemistry NZ Ltd
0.0035163776
PlusGroup Limited
0.0145858096
Pohatu Penguins
0.0203458204
Polybatics Ltd.
0.0128746139
Porirua City Council
0.0308851034
Ports of Auckland Limited
0.0482699631
Positive Thinking Ltd
0.0230236317
Possum Observatory
0.0069860932
Potter Building Services Ltd.
0.0695687692
Power Co Ltd.
0.0460472634
Power Systems Consultants New Zealand Ltd
0.0007332456
PowerbyProxi Ltd.
0.0092094527
Powerhouse Ventures Ltd
0.0168993386
Practitioners First Limited
0.0498031771
Presbyterian Church of New Zealand
0.0568509437
PriceWaterhouse Coopers (PwC)
0.0871589088
Priestley Structural Engineering
0.0638562314
Private Endodontic Practice
0.0308851034
ProCare Health Limited
0.0402932634
Prohealth Physiotherapy Ltd
0.0191984654
Promisia Ltd
0.0336423765
Proteus Wildlife Research Consultants
0.0129373969
Psychological Service
0.0460472634
Psychology Centre
0.0293398089
Pultron Composites Ltd.
0.0021164695
Pyrotek
0.0087282370
Q-Bit Ltd.
0.0198514744
QE Health
0.0568509437
Qnique Ltd
0.0902697988
QStar Solutions Ltd.
0.0043343552
Quadradix
0.0460472634
Quay Park Medical Centre
0.0823342069
Queens Academic Group
0.0230236317
Quest Integrity Group Ltd.
0.0270054146
Quigley and Watts Ltd.
0.0252390086
Quin Environmentals(NZ) Ltd.
0.0343539908
Quintessence Developments Ltd.
0.0178906864
Quit Group
0.0529746407
Radiata Pine Breeding Company
0.0009908660
Radio Spectrum Management
0.0276791693
Rakon Ltd.
0.0153490878
Rangiora New Life School
0.0379879851
Rape Prevention Education-Whakatu Mauri
0.0385538603
Rauawaawa Kaumatua Charitable Trust
0.0832485440
Raukatauri Music Therapy Centre
0.0460472634
Raukura Hauora O Tainui Trust
0.0092424538
Rayonier New Zealand Ltd
0.0258847376
Refugees as Survivors New Zealand
0.0568509437
Reid Construction Systems Ltd
0.0186146975
Renewable Energy
0.0039634640
Repromed
0.1161483663
Reserve Bank of New Zealand
0.0508886384
Resilient Organisations
0.0507825179
Resource Teacher: Learning and Behaviour
0.0460472634
Revolution Fibres Ltd
0.0784942708
Riccarton Rotary
0.0000000000
Risk Strategies Research and Consulting
0.0074309772
Rivuli Development
0.0089554611
RML Engineering
0.0087353529
Roche Products Limited
0.0568509437
Rockwell Automation
0.0460472634
Rolleston Veterinary Clinic
0.0726522686
Ropata Village Medical Centre
0.0705696678
Rotorua General Practice Group
0.0769323668
Rowe Davies Research Ltd
0.0260816842
Royal Australian and New Zealand College of Psychiatrists
0.0460472634
Royal Forest and Bird Protection Society of New Zealand
0.0240634410
Royal New Zealand College of General Practitioners
0.0678757259
Royal New Zealand Plunket Society
0.0534802418
Royal Society of New Zealand
0.0890977766
Ruaimoko Productions and Consultancy Ltd.
0.0154425517
Rumenz Ltd
0.0484310657
RuralLink
0.0087353529
[ reached getOption("max.print") -- omitted 511 entries ]
$value
[1] 21.71682
$options
$options$bmat
[1] "I"
$options$n
[1] 1511
$options$which
[1] "LA"
$options$nev
[1] 1
$options$tol
[1] 0
$options$ncv
[1] 0
$options$ldv
[1] 0
$options$ishift
[1] 1
$options$maxiter
[1] 3000
$options$nb
[1] 1
$options$mode
[1] 1
$options$start
[1] 1
$options$sigma
[1] 0
$options$sigmai
[1] 0
$options$info
[1] 0
$options$iter
[1] 3
$options$nconv
[1] 1
$options$numop
[1] 40
$options$numopb
[1] 0
$options$numreo
[1] 27top_10_eig2 <- tail(sort(eig2$vector),10)
top_10_eig2 NIWA University of Waikato AUT University
0.1576988 0.1897041 0.1992335
Canterbury District Health Board Auckland District Health Board Victoria University of Wellington
0.2127479 0.2346215 0.2896466
University of Canterbury Massey University University of Otago
0.3085040 0.4043171 0.6707261
University of Auckland
1.0000000 bottom_10_eig2 <- head(sort(eig2$vector),10)
bottom_10_eig2 Alzheimers Northland AP EnerTec Ltd.
0 0
Aviation Industry Association of New Zealand Inc Bio Soil and Crop Ltd
0 0
Blues Rugby Club Bruce Shallard and Associates
0 0
ChangeMakers Refugee Forum Chatham Rock Phosphate Ltd.
0 0
Chilton Saint James School Crown Fibre Holdings Limited
0 0 Вывод: Минимальные значения центральностей по
собственному значению также составляют 0. Наибольшую же
имеет университет Окленда. Его высокий показатель говорит, что сам
университет связан со многими вершинами, которые в свою очередь имеют
также высокое значение центральности.
Выводы
# объединим все центральности в один датафрейм и посмотрим корреляции в двух вариантах
df1 <- data.frame(deg, clos1, betw1, eig1$vector)
cor(df1) deg clos1 betw1 eig1.vector
deg 1.00000000 -0.03452649 0.96148582 0.8926645
clos1 -0.03452649 1.00000000 -0.01592647 -0.1091064
betw1 0.96148582 -0.01592647 1.00000000 0.7596773
eig1.vector 0.89266448 -0.10910642 0.75967732 1.0000000df2 <- data.frame(deg, clos2, betw2, eig2$vector)
cor(df2) deg clos2 betw2 eig2.vector
deg 1.00000000 -0.03349182 0.90929438 0.8418800
clos2 -0.03349182 1.00000000 -0.01198628 -0.1332681
betw2 0.90929438 -0.01198628 1.00000000 0.7737961
eig2.vector 0.84188004 -0.13326806 0.77379607 1.0000000Вывод: Составив корреляционные матрицы заметим, что существует высокая корреляция между следующими парами центральностей вершин: по степени - по кратчайшему расстоянию, по степени - по собств. значению и по собств. значению - по кратчайшему расстоянию
Сравним, какие организации попадали в топы по центральностям (исключая центральность по близости).
corr1 <- data.frame(
names(top_10_degree),
names(top_10_betw1),
names(top_10_eig1)
)
corr1
corr2 <- data.frame(
names(top_10_degree),
names(top_10_betw2),
names(top_10_eig2)
)
corr2Выводы по Заданию 3: Сравнив топы по максимальным центральностям (за исключением топа центральностей по близости из-за малого количества соседей [порядка 1]), заметим, что по трем центральностям первую пятерку занимают одни и те же организации: университет Окленда, университет Отаго, университет Мэсси, университет Кантербери и Викторианский университет Веллингтона.
Задание 4
В Задании 4 нам предлагается рассчитать ассортативность и гомофилию для графа. Начнем исследование данных с ассортативности:
Ассортативность
# Возникли проблемы с вычислением ассортативности через
# assortativity_nominal(net, types=V(net)$type, directed=F)
# Предупреждение: в результате преобразования созданы NA
# [1] NaN
assortativity_nominal(net, types=V(net)$type, directed=F)Предупреждение: в результате преобразования созданы NA[1] NaN# Поэтому было принято решение создать новый столбец с закодированными строками
V(net)$num_type <- ifelse( V(net)$type=="Business Enterprise", 1,
ifelse( V(net)$type=="Private not for profit", 2,
ifelse( V(net)$type=="Government", 3,
ifelse( V(net)$type=="Higher Education", 4, 0)
)
)
)assort_nom <- assortativity_nominal(net, types=V(net)$num_type, directed=F)
assort_nom # -0.05876298[1] -0.05876298# значение ассортативности не зависит от конкретных чисел
V(net)$num_type1 <- ifelse( V(net)$type=="Business Enterprise", 2,
ifelse( V(net)$type=="Private not for profit", 7,
ifelse( V(net)$type=="Government", 5,
ifelse( V(net)$type=="Higher Education", 10, 0)
)
)
)assortativity_nominal(net, types=V(net)$num_type1, directed=F) # -0.05876298[1] -0.05876298Обобщение результатов: Ассортативность в графе по типу вершин примерно равна -0.059. Это означает, что мы не можем утверждать наличие предпочтительного присоединения узлов сети к своему типу (среди узлов в общем, т.е. среди узлов всех типов).
Ассортативность по степени вершины составляет примерно -0.336, что говорит о предпочтительном присоединении узлов к вершинам с относительно небольшим количеством соседей.
Для выявления более точного эффекта предпочтительного присоединения именно среди университетов (что интересует нас в рамках исследовательского вопроса) рассчитаем показатели гомофилии для университетов и других типов институтов.
Нами было принято решение рассчитать dyadicity (ее посчитаем
только для одного случая, т.к. она не будет меняться при различных
разбиениях) и heterophilicity учреждений высшего образования
для следующих разделений на подгруппы: - Higher Education
vs все остальные - Higher Education vs
Business Enterprise - Higher Education vs
Government.
Влиянием Private not for profit можно пренебречь.
Higher Education vs все остальные
p <- edge_density(net)
p # 0.003745601[1] 0.003745601n_c <- sum( V(net)$type == 'Higher Education' )
n_c # 54[1] 54exp_diad_uni <- n_c * (n_c - 1) / 2 * p
exp_diad_uni # 5.359955[1] 5.359955unis <- V(net)[which( V(net)$type == 'Higher Education' )]
unis <- names(unis)
# unis
m_c <- 0
for (row in 1:nrow(edges)) {
from_obj <- edges[row, 'from']
to_obj <- edges[row, 'to']
if ( (from_obj %in% unis) && (to_obj %in% unis) ) {
m_c <- m_c + 1
}
}
m_c # 172[1] 172diadicity_uni <- m_c / exp_diad_uni
diadicity_uni # 32.08982[1] 32.08982# 2-й способ посчитать dyadicity
uni_net <- induced_subgraph(
net,
v=V(net)[which( V(net)$type == 'Higher Education' )]
)
# uni_net
# V(uni_net)$type # проверяем, что все вершины в новом графе вузы
edge_density(net) # 0.003745601[1] 0.003745601edge_density(uni_net) # 0.1201957[1] 0.1201957edge_density(uni_net) / edge_density(net) # 32.08982[1] 32.08982n_c # 54[1] 54p # 0.003745601[1] 0.003745601n_nc <- sum( V(net)$type != 'Higher Education' )
n_nc # 1457[1] 1457exp_hetero_uni <- n_nc * n_c * p
exp_hetero_uni # 294.6964[1] 294.6964m_mixed <- 0
for (row in 1:nrow(edges)) {
from_obj <- edges[row, 'from']
to_obj <- edges[row, 'to']
if ( (from_obj %in% unis) && !(to_obj %in% unis) ) {
m_mixed <- m_mixed + 1
}
if ( !(from_obj %in% unis) && (to_obj %in% unis) ) {
m_mixed <- m_mixed + 1
}
}
m_mixed # 2051[1] 2051heterophilicity_uni <- m_mixed / exp_hetero_uni
heterophilicity_uni # 6.959706[1] 6.959706Higher Education vs
Business Enterprise
# uni_biz_net <- induced_subgraph(
# net,
# v=V(net)[which(
# (V(net)$type == 'Higher Education') || (V(net)$type == 'Business Enterprise')
# )]
# )
uni_biz_net <- induced_subgraph(
net,
v=V(net)[which( V(net)$type %in% c('Higher Education', 'Business Enterprise') )]
)
# uni_biz_net
# V(uni_biz_net)$type
uni_wout_biz_net <- induced_subgraph(
uni_biz_net,
v=V(uni_biz_net)[which( V(uni_biz_net)$type == 'Higher Education' )]
)
# uni_wout_biz_net
# V(uni_wout_biz_net)$type
p_uni_vs_biz <- edge_density(uni_biz_net)
p_uni_vs_biz # 0.003036165[1] 0.003036165edge_density(uni_wout_biz_net) # 0.1201957[1] 0.1201957dyadicity_uni_vs_biz <- edge_density(uni_wout_biz_net) / p_uni_vs_biz
dyadicity_uni_vs_biz # 39.58799[1] 39.58799n_c # 54[1] 54p_uni_vs_biz # 0.003036165[1] 0.003036165n_nc_biz <- sum( V(net)$type == 'Business Enterprise' )
n_nc_biz # 1010[1] 1010exp_hetero_uni_vs_biz <- n_nc_biz * n_c * p_uni_vs_biz
exp_hetero_uni_vs_biz # 165.5925[1] 165.5925biz <- V(net)[which( V(net)$type == 'Business Enterprise' )]
biz <- names(biz)
# biz
m_mixed_vs_biz <- 0
for (row in 1:nrow(edges)) {
from_obj <- edges[row, 'from']
to_obj <- edges[row, 'to']
if ( (from_obj %in% unis) && (to_obj %in% biz) ) {
m_mixed_vs_biz <- m_mixed_vs_biz + 1
}
if ( (from_obj %in% biz) && (to_obj %in% unis) ) {
m_mixed_vs_biz <- m_mixed_vs_biz + 1
}
}
m_mixed_vs_biz # 1139[1] 1139heterophilicity_uni_vs_biz <- m_mixed_vs_biz / exp_hetero_uni_vs_biz
heterophilicity_uni_vs_biz # 6.878333[1] 6.878333Higher Education vs Government
uni_gov_net <- induced_subgraph(
net,
v=V(net)[which( V(net)$type %in% c('Higher Education', 'Government') )]
)
# V(uni_gov_net)$type
uni_wout_gov_net <- induced_subgraph(
uni_gov_net,
v=V(uni_gov_net)[which( V(uni_gov_net)$type == 'Higher Education' )]
)
# V(uni_wout_gov_net)$type
p_uni_vs_gov <- edge_density(uni_gov_net)
p_uni_vs_gov # 0.04231381[1] 0.04231381edge_density(uni_wout_gov_net) # 0.1201957[1] 0.1201957dyadicity_uni_vs_gov <- edge_density(uni_wout_gov_net) / p_uni_vs_gov
dyadicity_uni_vs_gov # 2.840578[1] 2.840578n_c # 54[1] 54p_uni_vs_gov # 0.04231381[1] 0.04231381n_nc_gov <- sum( V(net)$type == 'Business Enterprise' )
n_nc_gov # 1010[1] 1010exp_hetero_uni_vs_gov <- n_nc_gov * n_c * p_uni_vs_gov
exp_hetero_uni_vs_gov # 2307.795[1] 2307.795gov <- V(net)[which( V(net)$type == 'Business Enterprise' )]
gov <- names(gov)
# gov
m_mixed_vs_gov <- 0
for (row in 1:nrow(edges)) {
from_obj <- edges[row, 'from']
to_obj <- edges[row, 'to']
if ( (from_obj %in% unis) && (to_obj %in% gov) ) {
m_mixed_vs_gov <- m_mixed_vs_gov + 1
}
if ( (from_obj %in% gov) && (to_obj %in% unis) ) {
m_mixed_vs_gov <- m_mixed_vs_gov + 1
}
}
m_mixed_vs_gov # 0.4935447[1] 1139heterophilicity_uni_vs_gov <- m_mixed_vs_gov / exp_hetero_uni_vs_gov
heterophilicity_uni_vs_gov # 0.4935447[1] 0.4935447Соберем полученные значения dyadicity и
heterophilicity вместе: - Higher Education vs все
остальные: - dyadicity: 32.0898241 - heterophilicity: 6.9597056 -
Higher Education vs Business Enterprise: -
dyadicity: 39.5879866 - heterophilicity: 6.8783329 -
Higher Education vs Government: - dyadicity:
2.840578 - heterophilicity: 0.4935447.
Мы видим, что dyadicity университетов при разделении на университеты и всех остальных (а также при разделении на университеты и бизнес) очень высокая. При этом heterophilicity также доволльно сильно превышает 1.
В чем может быть объяснение этой особенности данных? Как утверждается
в статье “Functional
dyadicity and heterophilicity of gene-gene interactions in statistical
epistasis networks”, описанный выше факт может быть связан с тем,
что вершины со значением метки 1 имеют большую
центральность \(\Rightarrow\) хорошо
связаны друг с другом и с вершинами другого типа.
В Задании 6 мы будем проверять гипотезу касательно высоких
степеней вершин типа Higher Education среди крупных
университетов.
Выводы
Выводы по Заданию 4: Мы получили, что несмотря на плотные связи учреждений высшего образования между собой, по крайней мере некоторые из них имеют также прочные связи с другими типами организаций (в частности с бизнесом).
Задание 5
Проведем процедуру кластеризации вершин при помощи Edge-betweenness и Fast-greedy методов и сравним полученные результаты с существующей классификацией.
Т.к. считать кратчайший путь для исходных весов ребер является не очень осмысленным, используем обратные для исходных веса ребер.
Замечание: Для Fast-greedy не важно, какие данные использовать: исходные или инвертированные, т.к. этот метод не учитывает веса ребер (только их количество).
# проводим кластеризацию при помощи метода Edge-betweenness
ceb <- cluster_edge_betweenness(net, weights=E(net)$weight)Предупреждение: At core/community/edge_betweenness.c:493 : Membership vector will be selected based on the highest modularity score.# смотрим на полученные в результате кластеризации объекты
mbship_ceb <- membership(ceb)
# mbship_ceb
s_ceb <- sizes(ceb)
s_cebCommunity sizes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
45 213 233 154 229 190 75 46 164 48 32 2 2 2 3 15 2 2 8 2 2 4 2 2 2 2
27 28 29 30 31 32 33 34 35 36 37 38
7 2 2 2 2 2 2 2 2 2 3 2 ms_ceb <- modularity(ceb)
ms_ceb # 0.527262[1] 0.527262# ceb# > s_ceb <- sizes(ceb)
# > s_ceb
# Community sizes
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
# 45 213 233 154 229 190 75 46 164 48 32 2 2 2 3 15 2 2 8 2
# 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
# 2 4 2 2 2 2 7 2 2 2 2 2 2 2 2 2 3 2 # > ms_ceb <- modularity(ceb)
# > ms_ceb
# [1] 0.527262Визуализация кластеризации методом Edge-betweenness:
plot(
ceb, net,
vertex.label=NA,
vertex.color=V(net)$color,
layout=layout_nicely
)
plot(
ceb, net,
vertex.label=NA,
vertex.color=V(net)$color,
layout=layout_with_lgl
)
Сравним результаты кластеризации Edge-betweenness и имеющуюся классификацию вершин:
compare(ceb, V(net)$type, method='nmi') # [1] 0.03399001# здесь и далее мы используем нормализованное значение функции compare() для облегчения интерпретации возвращаемого результатаТаким образом, мы видим, что имеющаяся классификация вершин совсем не похожа на то, что мы получили при кластеризации. По всей видимости, “разделение по бутылочному горлышку” является не очень хорошим способом для кластеризации вершин в нашем датасете.
# проводим кластеризацию при помощи метода Fast-greedy
cfg <- cluster_fast_greedy(net, weights=E(net)$weight)
# смотрим на полученные в результате кластеризации объекты
mbship_cfg <- membership(cfg)
# mbship_cfg
s_cfg <- sizes(cfg)
s_cfgCommunity sizes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
219 144 212 132 141 94 189 120 84 82 28 3 2 15 3 3 2 2 2 2 2 2 2 2 2 2
27 28 29 30 31 32 33 34 35 36
2 2 2 2 2 2 2 2 2 2 ms_cfg <- modularity(cfg)
ms_cfg # 0.5310055[1] 0.5310055# cfg# > s_cfg <- sizes(cfg)
# > s_cfg
# Community sizes
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
# 219 144 212 132 141 94 189 120 84 82 28 3 2 15 3 3 2 2 2 2 2 2 2 2 2 2
# 27 28 29 30 31 32 33 34 35 36
# 2 2 2 2 2 2 2 2 2 2 # > ms_cfg <- modularity(cfg)
# > ms_cfg
# [1] 0.5310055Визуализация кластеризации методом Fast-greedy:
plot(
cfg, net,
vertex.label=NA,
vertex.color=V(net)$color,
layout=layout_nicely
)
plot(
cfg, net,
vertex.label=NA,
vertex.color=V(net)$color,
layout=layout_with_lgl
)
compare(cfg, V(net)$type, method='nmi') # 0.03386511[1] 0.03386511Таким образом, мы видим, что так же, как и предыдущий способ кластеризации, Fast-greedy не очень хорошо соответствует реальной классификации рассматриваемых институтов.
Выводы
Вывод по Заданию 5: Известные нам способы кластеризации (Edge-betweenness и Fast-greedy) не дали результата, похожего на имеющуюся в датасете классификацию.
Задание 6
Изначально был поставлен исследовательский вопрос, насколько активно при написании научных работ университеты Новой Зеландии взаимодействуют с другими типами организаций, нужно ли им как-то в этом способстовать извне (например, создавать общие лаботарии с индустриальными корпорациями и государственными органами). Помимо расчета значений гомофилии и различных видов центральностей, для ответа на заданный вопрос нам может помочь модель предсказания класса вершин Relational Neighbors Classifier (RNC).
Разделим все вершины на 2 класса: “1” - университет, “0” - иначе.
Отберем из каждого класса по 10 вершин и положим вероятности их
принадлежности первому классу соответственно 1 и
0. Для всех остальных вершин (unknown) положим
эту вероятность равной 0.5. При каждой итерации будем
обновлять вероятности каждой вершины исходя из вероятностей её соседей.
В итоге, после 10 таких итераций получим для каждой вершины вероятность
её принадлежности классу “1”, и отберем те вершины, чья вероятность
больше порога 0.5 в качестве принадлежащих классу “1”.
Для избежания случайности повторим этот алгоритм 100 раз и построим гистограмму распределения числа предсказанных университетов, а также гистограмму распределения средних вероятностей принадлежности группе университетов.
res <- rep(NA, 20)
pr <- rep(NA, 20)
for (j in 1:20){
network <- net
V(network)[which( V(network)$type == 'Higher Education' )]$type = 1
V(network)[which(V(network)$type != 1)]$type = 0
# вероятность вершины перейти в класс churn = 1 равна доле соседей churn = 1 от общего числа соседей
# используем матричные вычисления
random_uni <- sample( V(network)[ which(V(network)$type == 1) ], 10 )
random_not_uni <- sample( V(network)[ which(V(network)$type == 0) ], 10 )
for (i in 1:1511){
if (!(V(network)[i] %in% random_uni | (V(network)[i] %in% random_not_uni))){
V(network)$type[i] = 0.5
}
}
UniProb <- as.numeric(V(network)$type)
threshold <- 0.5
A <- as_adjacency_matrix(network)
A <- as.matrix(A)
Neighbors <- rowSums(A) # общее число соседей вершины
UniProb_iter <- UniProb
for(i in 1:10){
UniProb_iter <- as.vector((A %*% UniProb_iter) / Neighbors)
}
res[j] <- length(which(UniProb_iter > threshold))
pr[j] <- mean(UniProb_iter)
}hist(res, main='Число предсказанных университетов')
hist(pr, main='Средняя вероятность принадлежности классу 1')
Как можно увидеть, почти во всех случаях абсолютное число вершин предсказанj в качестве университетов. Получаем, что какие бы 10 университетов мы ни взяли, их класс дойдет до большинства вершин быстрее, чем противоположный класс 10 случайных вершин. Это распространяется и на случай, когда были выбраны наименее центральные университеты. Если бы университеты были плохо связаны с организациями другого типа, то их класс намного слабее распространялся бы на вершины другого типа, а это не так.
Значит, по крайней мере какие-то университеты (а именно наиболее центральные) довольно активно кооперируются с другими организациями (как, например, это делает Оклендский университет). Поэтому для таких университетов нет необходимости строить совместные с бизнесом и государством научные центры.
Вспомним про высокий показатель dyadicity у ВУЗов: выходит, что он получается таким большим из-за высокой гомофилии более мелких учебных заведений. Тогда можно предположить, что именно они плохо взаимодействуют с бизнесом и гос. органами.
Заключение
Как тогда можно им помочь? При моделировании их класс распространялся по сети через их соседей — крупные университеты. В таком случае, более разумно строить научные центры именно соединяющие мелкие университеты с крупными. Данным образом, казалось бы, усиливая гомофилию, мы, наоборот, будем способстовать развитию научных отношений университетов с индустриальными партнерами.
- Замечание
-
Здесь мы предполагаем эталонность крупных университетов (например, Оклендского) с точки зрения эффективности взаимодействия, а также качества и количества научных работ, что продемонстрировано, например, в этой статье.
---
title: "Дз по Сетевым моделям"
output:
  pdf_document: default
  author: "Кабанов Илья, Сухов Александр, Сысоев Никита"
  html_notebook: default
---

## Подготовительные шаги

```{r}
# Установим рабочую директорию
setwd("~/Documents/GitHub/RProjects_EF/Networks")
```

```{r}
# Подгрузим необходимые для дальнейшего анализа библиотеки
## install.packages("igraph")
## install.packages("igraphdata")
## install.packages("ggraph")
## install.packages("tidygraph")
## install.packages("DescTools")


library(igraph);
library(igraphdata);
library(ggraph);
library(tidygraph);
library(DescTools);
```

## Обработка данных и создание графа

```{r}
# Загрузим данные для исследования: набор ребер и вершин
edges <- read.csv("edges_1.csv", header=T) 
colnames(edges) <- c('from', 'to', 'type1', 'type2', 'weight')

nodes <- unique(edges[c('from', 'type1')])
more_nodes <- unique(edges[c('to', 'type2')])

colnames(nodes) <- c('organisation', 'type')
colnames(more_nodes) <- c('organisation', 'type')

nodes <- rbind(nodes, more_nodes)
nodes <- unique(nodes[c('organisation', 'type')])
rownames(nodes) <- NULL
edges <- edges[c('from', 'to', 'weight')]

# Создадим также набор обратных величин для весов ребер (это пригодится нам в дальнейшем). Исходные веса нам уже не понадобятся
edges$weight <- 1 / edges$weight

net <- graph_from_data_frame(d=edges, vertices=nodes, directed=F)

V(net)$color <- ifelse( V(net)$type=="Business Enterprise", "red", 
  ifelse( V(net)$type=="Private not for profit", "purple", 
    ifelse( V(net)$type=="Government", "green", 
      ifelse( V(net)$type=="Higher Education", "blue", "black") 
    ) 
  ) 
)
head(V(net)$color, 10)
```

**Поясним, почему в дальнейшем будем работать именно с обратными весами:** Кратчайший путь и кратчайшее расстояние в данной задаче будут представлять собой не то же самое, что и в задаче с издержками перевозок или длинами расстояний между вершинами в качестве весов ребер. Отрицательные веса мы не используем, потому что *алгоритм Дейкстры* работает с неотрицательными весами ребер, поэтому далее мы оперируем с обратными весами, т.к., на наш взгляд, этот выбор является наиболее оптимальным для преодоления возникших трудностей.

------------------------------------------------------------------------

## Исследовательский вопрос

**Исследовательский вопрос:** Какие есть способы улучшения взаимодействия учреждений высшего образования Новой Зеландии (если это вообще требуется)?

Наше исследование показывает, что возможно повысить эффективность небольших университетов посредством увеличения сотрудничества с крупными, которые в свою очередь имеют тесное сотредничество с бизнесом.

Детали см. в *Задании 6*.

------------------------------------------------------------------------

## Анализ датасета

### Описание датасета

Датасет представляет из себя множество вершин с качественными характеристиками и множество ребер с числовыми характеристиками (весами).

Вершинами являются организации Новой Зеландии, которые занимаются написанием научных статей в качестве одного из видов деятельности. Качественной характеристикой вершин является вид организации (государственная организации, высшее учебное заведение, коммерческое предприятие и частное некоммерческое предприятие). Всего в датасете 1511 вершин.

Между `i`-ой и `j`-ой вершинами (организациями) существует ребро, если за период 2010-2015 гг. на Scopus была опубликована хотя бы одна статья, хотя бы один автор которой числится в организации `i`, а другой автор -- в организации `j`. Всего в датасете 4273 ребра.

Вес ребра равен количеству совместных опубликованных научных работ. Если вес ребра между `i`-ой и `j`-ой вершиной равен 3, то это означает, что за указанный период на Scopus было опубликовано 3 научные работы, у которых хотя бы один автор числится в организации `i`, а другой --- в организации `j`.

------------------------------------------------------------------------

### Задание 2

При использовании нескольких пакетов для работы с графами не оказалось возможным интерпретируемо визуализировать граф полностью. Поэтому для отображения структуры нашей сети найдем 100 самых центральных по степени вершин и представим связи между ними при помощи пакета `ggraph`.

```{r}
V(net)$degrees <- degree(net)
nodes$degrees <- V(net)$degrees

for_vis_n <- nodes[order(-nodes$degrees),][1:100, 1:2]
for_vis_e <- edges[(edges$from %in% for_vis_n$organisation & edges$to %in% for_vis_n$organisation),]

for_vis_net <- graph_from_data_frame(d=for_vis_e, vertices=for_vis_n, directed=F)
V(for_vis_net)$degrees <- degree(for_vis_net)

for_vis_net %>%
  ggraph(layout='graphopt') +
  geom_node_point(aes(color = type, size=round(degrees/20))) +
  geom_edge_link(alpha = 0.05) +
  theme_void() +
  ggtitle("Network of New Zealand organisations")
```

Как можно увидеть, среди 100 самых центральных вершин с количественной точки зрения преобладают организации государственного сектора, однако самыми крупными здесь являются новозеландские университеты. Первые 5 мест по числу совместных научных работ принадлежат именно им, лидером по данному показателю является *Университет Окленда*, самый крупный и престижный университет Новой Зеландии.

Рассчитаем **базовые параметры** нашего графа. Так как весами дуг в данном случае является число совместных работ, то есть "сила связи" двух вершин, будем использовать обратные веса для подсчета центральностей через кратчайшие пути. Это довольно разумно, так как от написания дополнительной общей работы прирост в силе связи двух организаций должен монотонно снижаться, как и разница в пути до соседа.

```{r}
#Считаем базовые параметры графа

# Density
# The proportion of present edges from all possible ties.
p <- edge_density(net)

# связность сети
no <- igraph::components(net)$no # в пакете statnet такое же название
csize <- igraph::components(net)$csize
csize


# Diameter (longest geodesic distance) (если несколько компонент, то диаметр самой большой)
# Note that edge weights are used by default, unless set to NA.
diam <- diameter(net, weights=NA)
diam_w <- diameter(net)
path <- get_diameter(net, weights=NA)
path_w <- get_diameter(net)
path
path_w

# рассчитаем кратчайшие пути
# Average path length 
# The mean of the shortest distance between each pair of nodes in the network 
# (in both directions for directed graphs). 
m_dist <- mean_distance(net, weights=NA)
m_dist_w <- mean_distance(net)
```

Плотность нашего графа составляет `r round(p, 4)`. Такая низкая плотность (вероятность образования связи) довольно естественная для вероятности написания научной работы. Наша сеть имеет `r no` компонент связности: одна главная, соединяющая практически все вершины, а все остальные имеют по 2-3 вершины. Диаметр (наибольший из кратчаших путей) имеет длину `r round(diam_w, 2)`, или `r diam`, если брать единичные веса для всех дуг.

**Изучим соседство самой центральной вершины --- Оклендского Университета** (с кем чаще всего взаимодействует наиболее престижный ВУЗ страны):

```{r}
# We can also easily identify the immediate neighbors of a vertex.
# The 'neighbors' function finds all nodes one step out from the focal actor.
# To find the neighbors for multiple nodes, use 'adjacent_vertices()'.
d <- data.frame(neighbors(net, V(net)["University of Auckland"], mode="total")$type)
groups <- as.data.frame(table(d))[, 2]
pie(groups, labels=paste0(as.data.frame(table(d))[, 1], ', ',round(groups/sum(groups)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Neighbors of University of Auckland')

```

```{r}
# To find node neighborhoods going more than one step out, use function 'ego()'
# with parameter 'order' set to the number of steps out to go from the focal node(s).
neigh2 <- data.frame(ego(net, order = 2, nodes = V(net)["University of Auckland"])[[1]]$type)
groups2 <- as.data.frame(table(neigh2))[, 2]
pie(groups2, labels=paste0(as.data.frame(table(neigh2))[, 1], ', ',round(groups2/sum(groups2)*100, digits=1), '%'), 
    col=c(5, 2, 3, 4), main='Two-step neighbors of University of Auckland')
```

Довольно ожидаемо, что чаще всего в написании научных работ такой успешный университет сотрудничает с индустрией. **Это подтвеждает наше предположение о том, успех научной работы зависит от работы с бизнесом.** В ближайшем окружении данной организации также принято вести исследования с индустрией.

**Сравним нашу сеть с теоритическими моделями случайного графа** на основе *распределения числа их соседей*, *диаметра*, с*реднего кратчайшего пути* и *числа компонент связности*. Начнем с модели случайного графа *Эрдеша-Реньи*.

```{r}
#Генерируем модели случайного графа erdos.renyi
p <- edge_density(net)

random_model <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- erdos.renyi.game(n=gorder(net), p.or.m=p, type='gnp')
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

Как можно заметить, **все рассматриваемые показатели нашей сети значимо отличаются от модельных**, значит, структуру нашей сети нельзя описать данным образом.

**Обратимся к модели "Малого мира"** с регулярной решеткой. Однако в этом случае сперва нужно подобрать гиперпараметр --- долю переприсоединенных дуг.

```{r}
#Генерируем модели случайного графа с регулярной решеткой
n_of_nei <- mean(degree(net))
diam_net <- diameter(net, weights=NA)
#Ищем оптимальное значение p
mean_dist_net <- mean_distance(net)
model <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
res <- rep(NA, 100)
for (i in 1:100){
  model[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = i/100)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

# p = 0.99

random_model <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 30)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_smallworld(dim = 1, size = gorder(net), nei = n_of_nei, p = 0.99)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

```{r}
# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

plot(x=c(1:40)/10, y=res)
#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)
```

**Аналогично предыдущему случаю, данная модель плохо описывает структуру нашего графа.** Значимо совпадает лишь диаметр, так как по нему в том числе происходил подбор гиперпараметра.

Рассмотрим также **схожесть с моделью Барабаши-Альберта**, включающей предпочтительное присоединение к наиболее центральным вершинам.

```{r}

# Генерируем модель Барабаши-Альберта
#Ищем оптимальное значение power
model <- vector('list', 100)
res <- rep(NA, 40)
m <- rep(NA, 100)
d <- rep(NA, 100)
for (i in c(1:40)){
  model[[i]] <- sample_pa(n = gorder(net), power = i/10, directed = FALSE)
  m[i] <- mean_distance(model[[i]])
  d[i] <- diameter(model[[i]])
  res[i] <- ((m[i]-mean_dist_net)^2+(d[i]-diam_net)^2)^(1/2) 
}

#power=2.15

random_model <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
par(mfrow = c(1, 2))
hist(degree(net), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
hist(degree(random_model), main = "Histogram of node degree", breaks = 1:vcount(net)-1, prob = TRUE, xlim=range(c(0, 20)))
par(mfrow = c(1, 1))

gl <- vector('list', 100)
m <- rep(NA, 100)
d <- rep(NA, 100)
a <- rep(NA, 100)
for (i in 1:100){
  gl[[i]] <- sample_pa(n = gorder(net), power = 2.15, directed = FALSE)
  m[i] <- mean_distance(gl[[i]])
  d[i] <- diameter(gl[[i]])
  a[i] <- igraph::components(gl[[i]])$no
}
mean_distance <- m
hist(mean_distance, xlim=range(c(min(m, mean_distance(net)), max(m, mean_distance(net)))))
abline(v=mean_distance(net), col='red', lty=3, lwd=2) 

diameter <- d
hist(diameter, xlim=range(c(min(d, diameter(net, weights=NA)), max(d, diameter(net, weights=NA)))))
abline(v=diameter(net, weights=NA), col='red', lty=3, lwd=2) 

number_of_components <- a
hist(number_of_components, xlim=range(c(0, 25)))
abline(v=igraph::components(net)$no, col='red', lty=3, lwd=2)

```

Как мы получили, данная модель тоже не подходит для описания структуры новозеландской сети: все статистически значимо отличается, кроме параметра, по которому проходил подбор гиперпараметра.

#### Выводы

**Выводы по *Заданию 2*:** Ни одна из теоретических моделей, известных нам, не описывает структуры нашего графа достаточно точно.

------------------------------------------------------------------------

### Задание 3

В этом задании нам предлагается посчитать различные меры *центральности вершин* и сделать содержательные выводы на основе полученных расчетов.

Замечание

:   Для анализа используем обратные веса, т.к. их использование делает осмысленным расчет центральности по близости и кратчайшему пути, но не искажает остальных мер центральности вершин.

#### Центральность по степени

Для начала посчитаем **центральность по степени**:

```{r}
deg <- degree(net)

# plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=deg)
```

Теперь построим *гистограмму распределения степеней вершин*:

```{r}
# гистограмма степеней вершин
hist(deg, main="Histogram of node degree", breaks=50, prob=TRUE) 
# распределение степеней вершин

mean(deg) # Средняя степень вершины по графу
# ~ 5.66
Mode(deg) # Модальная степень вершин графа
# 1 -> 599 раз
median(deg) # Медиана степеней вершин
# ~ 2
top_10_degree <- tail(sort(deg), 10) # топ-10 по степеням
top_10_degree # в топе - 7 университетов, 3 гос. учреждения
```

**Вывод:** Центральность вершин по степени не зависит от весов. Подавляющее большинство вершин имеет степень, меньшую `50`. Так, медиана кол-ва соседей равняется `r round(median(deg))`. В среднем у вершины такого графа степень равна `r round(mean(deg), 2)`. Наиболее часто встречающаяся степень вершины --- 1, которая встречается 599 раз. Если мы посмотрим 10 вершин с наибольшим числом соседей, то окажется, что 7 из них являются университетами, в числе которых крупнейший --- университет Окленда (степень вершины максимальная --- `r max(deg)`). Оставшиеся 3 организации являются государственными: 2 департамента здравоохранения и 1 исследовательская компания. Степень у всех вершин, входящих в топ-10, \> 100.

#### Центральность по близости

Далее рассчитаем **центральность по близости** двумя способами: В первом варианте все веса ребер графа являются `1`, в другом используются обратные веса ребер.

```{r}
clos1 <- closeness(net, weights=NA) # Первый способ - без учета весов
clos1

plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos1 * 50)
```

```{r}
top_10_clos1 <- tail(sort(clos1), 10) 
# Вектор-топ 42 также будет единичным, а вот вектор-топ 43 уже нет
top_10_clos1

bottom_10_clos1 <- head(sort(clos1), 10)
bottom_10_clos1

clos1["University of Auckland"]
```

```{r}
clos2 <- closeness(net)
clos2

plot(net, vertex.label=NA, layout=layout_with_fr, vertex.size=clos2 * 50)
```

```{r}
top_10_clos2 <- tail(sort(clos2), 10) 
top_10_clos2

bottom_10_clos2 <- head(sort(clos2), 10)
bottom_10_clos2

clos2["University of Auckland"]
```

**Вывод:** В обоих случаях максимальная центральность вершин будет составлять `1`. В нашем графе существует 21 пара вершин, которая связана лишь между собой и более ни с кем (из рассчета для графа с единичными весами ребер). Из них лишь 5 организаций работали совместно более 1 раза (из рассчета для графа с обратными весами). Топ-10 центральных вершин по близости и топ-10 по степени уже существенно различаются. Так, центральность по близости университета Окленда составит `r clos1["University of Auckland"]` в первом случае и `r clos1["University of Auckland"]`. Т.е. `round(1 / clos1["University of Auckland"])` или `round(1 / clos2["University of Auckland"])` --- сумма длин всех путей от университета Окленда до любой другой вершины в зависимости от метода рассчета.

#### Центральность по кратчайшему пути

```{r}
betw1 <- betweenness(net, weights=NA)
head(betw1)

top_10_betw1 <- tail(sort(betw1), 10)
top_10_betw1

bottom_10_betw1 <- head(sort(betw1), 10)
bottom_10_betw1

betw1["University of Auckland"]
```

```{r}
betw2 <- betweenness(net)
head(betw2)

top_10_betw2 <- tail(sort(betw2), 10)
top_10_betw2

bottom_10_betw2 <- head(sort(betw2), 10)
bottom_10_betw2

betw2["University of Auckland"]
```

**Вывод:** При разных методах минимальные значения центральности у вершин будут равны `0`. Это вершины, расположенные на периферии графа, или те, которые вовсе имеют всего одного соседа (например, та 21 пара вершин). Максимальные центральности вершин превышают `40 000` в топ-10. В обоих случаях университет Окленда на первом месте (`r max(betw1)` и `r max(betw2)`). Значительное число кратчайших путей между любыми двумя вершинами проходит именно через данный университет.

#### Центральность по собственному значению

```{r}
eig1 <- eigen_centrality(net, weights = NA)
head(eig1)

top_10_eig1 <- tail(sort(eig1$vector), 10)
top_10_eig1

bottom_10_eig1 <- head(sort(eig1$vector), 10)
bottom_10_eig1
```

```{r}
eig2 <- eigen_centrality(net)
head(eig2)

top_10_eig2 <- tail(sort(eig2$vector),10)
top_10_eig2

bottom_10_eig2 <- head(sort(eig2$vector),10)
bottom_10_eig2
```

**Вывод:** Минимальные значения центральностей по собственному значению также составляют `0`. Наибольшую же имеет университет Окленда. Его высокий показатель говорит, что сам университет связан со многими вершинами, которые в свою очередь имеют также высокое значение центральности.

#### Выводы

```{r}
# объединим все центральности в один датафрейм и посмотрим корреляции в двух вариантах 
df1 <- data.frame(deg, clos1, betw1, eig1$vector)
cor(df1)

df2 <- data.frame(deg, clos2, betw2, eig2$vector)
cor(df2)
```

**Вывод:** Составив корреляционные матрицы заметим, что существует высокая корреляция между следующими парами центральностей вершин: по степени - по кратчайшему расстоянию, по степени - по собств. значению и по собств. значению - по кратчайшему расстоянию

Сравним, какие организации попадали в топы по центральностям (исключая центральность по близости).

```{r}

corr1 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw1), 
  names(top_10_eig1)
)
corr1

corr2 <- data.frame(
  names(top_10_degree), 
  names(top_10_betw2), 
  names(top_10_eig2)
)
corr2
```

**Выводы по Заданию 3:** Сравнив топы по максимальным центральностям (за исключением топа центральностей по близости из-за малого количества соседей [порядка 1]), заметим, что по трем центральностям первую пятерку занимают одни и те же организации: университет Окленда, университет Отаго, университет Мэсси, университет Кантербери и Викторианский университет Веллингтона.

------------------------------------------------------------------------

### Задание 4

В *Задании 4* нам предлагается рассчитать *ассортативность* и *гомофилию* для графа. Начнем исследование данных с *ассортативности*:

#### Ассортативность

```{r}
# Возникли проблемы с вычислением ассортативности через
# assortativity_nominal(net, types=V(net)$type, directed=F) 
# Предупреждение: в результате преобразования созданы NA
# [1] NaN
assortativity_nominal(net, types=V(net)$type, directed=F)
```

```{r}
# Поэтому было принято решение создать новый столбец с закодированными строками

V(net)$num_type <- ifelse( V(net)$type=="Business Enterprise", 1, 
                          ifelse( V(net)$type=="Private not for profit", 2, 
                              ifelse( V(net)$type=="Government", 3, 
                                  ifelse( V(net)$type=="Higher Education", 4, 0) 
                              ) 
                          ) 
                       )
```

```{r}
assort_nom <- assortativity_nominal(net, types=V(net)$num_type, directed=F) 
assort_nom # -0.05876298
```

```{r}
# значение ассортативности не зависит от конкретных чисел
V(net)$num_type1 <- ifelse( V(net)$type=="Business Enterprise", 2, 
                           ifelse( V(net)$type=="Private not for profit", 7, 
                               ifelse( V(net)$type=="Government", 5, 
                                  ifelse( V(net)$type=="Higher Education", 10, 0) 
                               ) 
                           ) 
                        )
```

```{r}
assortativity_nominal(net, types=V(net)$num_type1, directed=F) # -0.05876298
```

```{r}
# считаем ассортативность по степени вершины
assort_deg <- assortativity_degree(net, directed=F) # -0.3361749
assort_deg
```

**Обобщение результатов:** *Ассортативность* в графе по типу вершин примерно равна `r round(assort_nom, 3)`. Это означает, что мы не можем утверждать наличие предпочтительного присоединения узлов сети к своему типу (среди узлов в общем, т.е. среди узлов всех типов).

*Ассортативность* по степени вершины составляет примерно `r round(assort_deg, 3)`, что говорит о предпочтительном присоединении узлов к вершинам с относительно небольшим количеством соседей.

> Для выявления более точного эффекта предпочтительного присоединения именно среди университетов (что интересует нас в рамках исследовательского вопроса) рассчитаем показатели гомофилии для университетов и других типов институтов.

Нами было принято решение рассчитать *dyadicity* (ее посчитаем только для одного случая, т.к. она не будет меняться при различных разбиениях) и *heterophilicity* учреждений высшего образования для следующих разделений на подгруппы: - `Higher Education` vs все остальные - `Higher Education` vs `Business Enterprise` - `Higher Education` vs `Government`.

<ins>Замечание:</ins>

Влиянием `Private not for profit` можно пренебречь.

#### `Higher Education` vs все остальные

```{r}
p <- edge_density(net)
p # 0.003745601
n_c <- sum( V(net)$type == 'Higher Education' )
n_c # 54
exp_diad_uni <- n_c * (n_c - 1) / 2 * p
exp_diad_uni # 5.359955

unis <- V(net)[which( V(net)$type == 'Higher Education' )]
unis <- names(unis)
# unis

m_c <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% unis) ) {
    m_c <- m_c + 1
  }
}

m_c # 172

diadicity_uni <- m_c / exp_diad_uni 
diadicity_uni # 32.08982
```

```{r}
# 2-й способ посчитать dyadicity
uni_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type == 'Higher Education' )] 
)
# uni_net
# V(uni_net)$type # проверяем, что все вершины в новом графе вузы

edge_density(net) # 0.003745601
edge_density(uni_net) # 0.1201957

edge_density(uni_net) / edge_density(net) # 32.08982
```

```{r}
n_c # 54
p # 0.003745601
n_nc <- sum( V(net)$type != 'Higher Education' )
n_nc # 1457

exp_hetero_uni <- n_nc * n_c * p
exp_hetero_uni # 294.6964

m_mixed <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && !(to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
  if ( !(from_obj %in% unis) && (to_obj %in% unis) ) {
    m_mixed <- m_mixed + 1
  }
}

m_mixed # 2051

heterophilicity_uni <- m_mixed / exp_hetero_uni
heterophilicity_uni # 6.959706
```

#### `Higher Education` vs `Business Enterprise`

```{r}
# uni_biz_net <- induced_subgraph( 
#   net, 
#   v=V(net)[which( 
#     (V(net)$type == 'Higher Education') || (V(net)$type == 'Business Enterprise') 
#       )] 
# )
uni_biz_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Business Enterprise') )] 
)
# uni_biz_net
# V(uni_biz_net)$type

uni_wout_biz_net <- induced_subgraph( 
  uni_biz_net, 
  v=V(uni_biz_net)[which( V(uni_biz_net)$type == 'Higher Education' )] 
)
# uni_wout_biz_net
# V(uni_wout_biz_net)$type


p_uni_vs_biz <- edge_density(uni_biz_net)
p_uni_vs_biz # 0.003036165
edge_density(uni_wout_biz_net) # 0.1201957

dyadicity_uni_vs_biz <- edge_density(uni_wout_biz_net) / p_uni_vs_biz 
dyadicity_uni_vs_biz # 39.58799
```

```{r}
n_c # 54
p_uni_vs_biz # 0.003036165
n_nc_biz <- sum( V(net)$type == 'Business Enterprise' )
n_nc_biz # 1010

exp_hetero_uni_vs_biz <- n_nc_biz * n_c * p_uni_vs_biz
exp_hetero_uni_vs_biz # 165.5925

biz <- V(net)[which( V(net)$type == 'Business Enterprise' )]
biz <- names(biz)
# biz

m_mixed_vs_biz <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% biz) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
  if ( (from_obj %in% biz) && (to_obj %in% unis) ) {
    m_mixed_vs_biz <- m_mixed_vs_biz + 1
  }
}

m_mixed_vs_biz # 1139

heterophilicity_uni_vs_biz <- m_mixed_vs_biz / exp_hetero_uni_vs_biz
heterophilicity_uni_vs_biz # 6.878333
```

#### `Higher Education` vs `Government`

```{r}
uni_gov_net <- induced_subgraph( 
  net, 
  v=V(net)[which( V(net)$type %in% c('Higher Education', 'Government') )] 
)
# V(uni_gov_net)$type

uni_wout_gov_net <- induced_subgraph( 
  uni_gov_net, 
  v=V(uni_gov_net)[which( V(uni_gov_net)$type == 'Higher Education' )] 
)
# V(uni_wout_gov_net)$type


p_uni_vs_gov <- edge_density(uni_gov_net) 
p_uni_vs_gov # 0.04231381
edge_density(uni_wout_gov_net) # 0.1201957

dyadicity_uni_vs_gov <- edge_density(uni_wout_gov_net) / p_uni_vs_gov 
dyadicity_uni_vs_gov # 2.840578
```

```{r}
n_c # 54
p_uni_vs_gov # 0.04231381
n_nc_gov <- sum( V(net)$type == 'Business Enterprise' )
n_nc_gov # 1010

exp_hetero_uni_vs_gov <- n_nc_gov * n_c * p_uni_vs_gov
exp_hetero_uni_vs_gov # 2307.795

gov <- V(net)[which( V(net)$type == 'Business Enterprise' )]
gov <- names(gov)
# gov

m_mixed_vs_gov <- 0

for (row in 1:nrow(edges)) {
  from_obj <- edges[row, 'from']
  to_obj <- edges[row, 'to']
  
  if ( (from_obj %in% unis) && (to_obj %in% gov) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
  if ( (from_obj %in% gov) && (to_obj %in% unis) ) {
    m_mixed_vs_gov <- m_mixed_vs_gov + 1
  }
}

m_mixed_vs_gov # 0.4935447

heterophilicity_uni_vs_gov <- m_mixed_vs_gov / exp_hetero_uni_vs_gov
heterophilicity_uni_vs_gov # 0.4935447
```

Соберем полученные значения *dyadicity* и *heterophilicity* вместе: - `Higher Education` vs все остальные: - dyadicity: `r diadicity_uni # 32.08982` - heterophilicity: `r heterophilicity_uni # 6.959706` - `Higher Education` vs `Business Enterprise`: - dyadicity: `r dyadicity_uni_vs_biz # 39.58799` - heterophilicity: `r heterophilicity_uni_vs_biz # 6.878333` - `Higher Education` vs `Government`: - dyadicity: `r dyadicity_uni_vs_gov # 2.840578` - heterophilicity: `r heterophilicity_uni_vs_gov # 0.4935447`.

Мы видим, что dyadicity университетов при разделении на университеты и всех остальных (а также при разделении на университеты и бизнес) очень высокая. При этом heterophilicity также доволльно сильно превышает 1.

В чем может быть объяснение этой особенности данных? Как утверждается в статье ["Functional dyadicity and heterophilicity of gene-gene interactions in statistical epistasis networks"](https://biodatamining.biomedcentral.com/articles/10.1186/s13040-015-0062-4), описанный выше факт может быть связан с тем, что вершины со значением метки `1` имеют большую центральность $\Rightarrow$ хорошо связаны друг с другом и с вершинами другого типа.

В *Задании 6* мы будем проверять гипотезу касательно высоких степеней вершин типа `Higher Education` среди крупных университетов.

#### Выводы

**Выводы по Заданию 4:** Мы получили, что несмотря на плотные связи учреждений высшего образования между собой, по крайней мере некоторые из них имеют также прочные связи с другими типами организаций (в частности с бизнесом).

------------------------------------------------------------------------

### Задание 5

Проведем процедуру кластеризации вершин при помощи Edge-betweenness и Fast-greedy методов и сравним полученные результаты с существующей классификацией.

Т.к. считать кратчайший путь для исходных весов ребер является не очень осмысленным, используем обратные для исходных веса ребер.

Замечание: Для Fast-greedy не важно, какие данные использовать: исходные или инвертированные, т.к. этот метод не учитывает веса ребер (только их количество).

```{r}
# проводим кластеризацию при помощи метода Edge-betweenness
ceb <- cluster_edge_betweenness(net, weights=E(net)$weight)

# смотрим на полученные в результате кластеризации объекты
mbship_ceb <- membership(ceb) 
# mbship_ceb

s_ceb <- sizes(ceb)
s_ceb

ms_ceb <- modularity(ceb)
ms_ceb # 0.527262
```

```{r}
# ceb
```

```{r}
# > s_ceb <- sizes(ceb)
# > s_ceb
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
#  45 213 233 154 229 190  75  46 164  48  32   2   2   2   3  15   2   2   8   2 
#  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38 
#   2   4   2   2   2   2   7   2   2   2   2   2   2   2   2   2   3   2 
```

```{r}
# > ms_ceb <- modularity(ceb)
# > ms_ceb
# [1] 0.527262
```

**Визуализация кластеризации методом Edge-betweenness:**

```{r}
plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)
```

```{r}
plot(
  ceb, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)
```

**Сравним результаты кластеризации Edge-betweenness и имеющуюся классификацию вершин:**

```{r}
compare(ceb, V(net)$type, method='nmi') # 
# здесь и далее мы используем нормализованное значение функции compare() для облегчения интерпретации возвращаемого результата
```

Таким образом, мы видим, что имеющаяся классификация вершин совсем не похожа на то, что мы получили при кластеризации. <mark> По всей видимости, "разделение по бутылочному горлышку" является не очень хорошим способом для кластеризации вершин в нашем датасете. </mark>

```{r}
# проводим кластеризацию при помощи метода Fast-greedy
cfg <- cluster_fast_greedy(net, weights=E(net)$weight) 

# смотрим на полученные в результате кластеризации объекты
mbship_cfg <- membership(cfg) 
# mbship_cfg

s_cfg <- sizes(cfg)
s_cfg

ms_cfg <- modularity(cfg)
ms_cfg # 0.5310055
```

```{r}
# cfg
```

```{r}
# > s_cfg <- sizes(cfg)
# > s_cfg
# Community sizes
#   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 
# 219 144 212 132 141  94 189 120  84  82  28   3   2  15   3   3   2   2   2   2   2   2   2   2   2   2 
#  27  28  29  30  31  32  33  34  35  36 
#   2   2   2   2   2   2   2   2   2   2 
```

```{r}
# > ms_cfg <- modularity(cfg)
# > ms_cfg
# [1] 0.5310055
```

**Визуализация кластеризации методом Fast-greedy:**

```{r}
plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_nicely
)
```

```{r}
plot(
  cfg, net, 
  vertex.label=NA, 
  vertex.color=V(net)$color, 
  layout=layout_with_lgl
)
```

```{r}
compare(cfg, V(net)$type, method='nmi') # 0.03386511
```

Таким образом, мы видим, что так же, как и предыдущий способ кластеризации, Fast-greedy не очень хорошо соответствует реальной классификации рассматриваемых институтов.

#### Выводы

**Вывод по Заданию 5:** Известные нам способы кластеризации (Edge-betweenness и Fast-greedy) не дали результата, похожего на имеющуюся в датасете классификацию.

------------------------------------------------------------------------

### Задание 6

Изначально был поставлен исследовательский вопрос, насколько активно при написании научных работ университеты Новой Зеландии взаимодействуют с другими типами организаций, нужно ли им как-то в этом способстовать извне (например, создавать общие лаботарии с индустриальными корпорациями и государственными органами). Помимо расчета значений гомофилии и различных видов центральностей, для ответа на заданный вопрос нам может помочь модель предсказания класса вершин *Relational Neighbors Classifier* (*RNC*).

Разделим все вершины на 2 класса: "1" - университет, "0" - иначе. Отберем из каждого класса по 10 вершин и положим вероятности их принадлежности первому классу соответственно `1` и `0`. Для всех остальных вершин (`unknown`) положим эту вероятность равной `0.5`. При каждой итерации будем обновлять вероятности каждой вершины исходя из вероятностей её соседей. В итоге, после 10 таких итераций получим для каждой вершины вероятность её принадлежности классу "1", и отберем те вершины, чья вероятность больше порога `0.5` в качестве принадлежащих классу "1".

Для избежания случайности повторим этот алгоритм 100 раз и построим гистограмму распределения числа предсказанных университетов, а также гистограмму распределения средних вероятностей принадлежности группе университетов.

```{r}
res <- rep(NA, 20)
pr <- rep(NA, 20)

for (j in 1:20){ 
  network <- net
  V(network)[which( V(network)$type == 'Higher Education' )]$type = 1
  V(network)[which(V(network)$type != 1)]$type = 0
  
  
  # вероятность вершины перейти в класс churn = 1 равна доле соседей churn = 1 от общего числа соседей
  # используем матричные вычисления
  random_uni <- sample( V(network)[ which(V(network)$type == 1) ], 10 )
  random_not_uni <- sample( V(network)[ which(V(network)$type == 0) ], 10 )
  
  
  for (i in 1:1511){
    if (!(V(network)[i] %in% random_uni | (V(network)[i] %in% random_not_uni))){
      V(network)$type[i] = 0.5
    }
  }
  
  UniProb <-  as.numeric(V(network)$type)
  threshold <- 0.5
  A <- as_adjacency_matrix(network)
  A <- as.matrix(A)
  Neighbors <- rowSums(A) # общее число соседей вершины
  
  UniProb_iter <- UniProb
  for(i in 1:10){
    UniProb_iter <- as.vector((A %*% UniProb_iter) / Neighbors)
  }
  res[j] <- length(which(UniProb_iter > threshold))
  pr[j] <- mean(UniProb_iter)
}
```

```{r}
hist(res, main='Число предсказанных университетов')
hist(pr, main='Средняя вероятность принадлежности классу 1')
```

Как можно увидеть, почти во всех случаях абсолютное число вершин предсказанj в качестве университетов. Получаем, что *какие бы 10 университетов мы ни взяли, их класс дойдет до большинства вершин быстрее, чем противоположный класс 10 случайных вершин*. Это распространяется и на случай, когда были выбраны наименее центральные университеты. Если бы университеты были плохо связаны с организациями другого типа, то их класс намного слабее распространялся бы на вершины другого типа, а это не так.

Значит, по крайней мере какие-то университеты (а именно наиболее центральные) довольно активно кооперируются с другими организациями (как, например, это делает Оклендский университет). Поэтому для таких университетов нет необходимости строить совместные с бизнесом и государством научные центры.

Вспомним про высокий показатель *dyadicity* у ВУЗов: выходит, что он получается таким большим из-за высокой гомофилии более мелких учебных заведений. Тогда можно предположить, что именно они плохо взаимодействуют с бизнесом и гос. органами.

------------------------------------------------------------------------

#### Заключение

Как тогда можно им помочь? При моделировании их класс распространялся по сети через их соседей --- крупные университеты. **В таком случае, более разумно строить научные центры именно соединяющие мелкие университеты с крупными. Данным образом, казалось бы, усиливая гомофилию, мы, наоборот, будем способстовать развитию научных отношений университетов с индустриальными партнерами.**

Замечание

:   Здесь мы предполагаем эталонность крупных университетов (например, Оклендского) с точки зрения эффективности взаимодействия, а также качества и количества научных работ, что продемонстрировано, например, в [этой статье](https://www.researchgate.net/publication/324091355_Why_Should_University_and_Business_Cooperate_A_Discussion_of_Advantages_and_Disadvantages).
